2.4.5 second order linear exact ode

Table 2.459: second order linear exact ode

#

ODE

CAS classification

Solved?

11

\[ {}x^{\prime \prime } = 50 \]
i.c.

[[_2nd_order, _quadrature]]

12

\[ {}x^{\prime \prime } = -20 \]
i.c.

[[_2nd_order, _quadrature]]

13

\[ {}x^{\prime \prime } = 3 t \]
i.c.

[[_2nd_order, _quadrature]]

14

\[ {}x^{\prime \prime } = 2 t +1 \]
i.c.

[[_2nd_order, _quadrature]]

15

\[ {}x^{\prime \prime } = 4 \left (3+t \right )^{2} \]
i.c.

[[_2nd_order, _quadrature]]

16

\[ {}x^{\prime \prime } = \frac {1}{\sqrt {t +4}} \]
i.c.

[[_2nd_order, _quadrature]]

17

\[ {}x^{\prime \prime } = \frac {1}{\left (t +1\right )^{3}} \]
i.c.

[[_2nd_order, _quadrature]]

18

\[ {}x^{\prime \prime } = 50 \sin \left (5 t \right ) \]
i.c.

[[_2nd_order, _quadrature]]

147

\[ {}x y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_y]]

150

\[ {}x y^{\prime \prime }+y^{\prime } = 4 x \]

[[_2nd_order, _missing_y]]

221

\[ {}y^{\prime \prime }+y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

236

\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

237

\[ {}2 y^{\prime \prime }+3 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

244

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

272

\[ {}2 y^{\prime \prime }-3 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

376

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

813

\[ {}y^{\prime \prime }+y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

825

\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

826

\[ {}2 y^{\prime \prime }+3 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

833

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

846

\[ {}2 y^{\prime \prime }-3 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

902

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1253

\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

1294

\[ {}t^{2} y^{\prime \prime }+4 t y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

1296

\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

1330

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

1345

\[ {}t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1352

\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1742

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

1746

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

1754

\[ {}\left (x^{2}-4\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

1811

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 2 x^{2}+2 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1828

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = x^{{3}/{2}} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1837

\[ {}\left (-1+x \right )^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 x \]
i.c.

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1839

\[ {}\left (x +1\right ) \left (2 x +3\right ) y^{\prime \prime }+2 \left (2+x \right ) y^{\prime }-2 y = \left (2 x +3\right )^{2} \]
i.c.

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

2362

\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

2363

\[ {}y^{\prime \prime }+t y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

2400

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

2433

\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

2435

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

2543

\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

2544

\[ {}y^{\prime \prime }+t y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

2581

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

2591

\[ {}t^{2} y^{\prime \prime }-2 y = t^{2} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

2607

\[ {}y^{\prime \prime }+2 y^{\prime } = 1+t^{2}+{\mathrm e}^{-2 t} \]

[[_2nd_order, _missing_y]]

2629

\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

2631

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

3089

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

3141

\[ {}2 y^{\prime \prime }+y^{\prime } = 8 \sin \left (2 x \right )+{\mathrm e}^{-x} \]
i.c.

[[_2nd_order, _missing_y]]

3217

\[ {}y^{\prime \prime }+2 y^{\prime } = x^{3} \sin \left (2 x \right ) \]

[[_2nd_order, _missing_y]]

3218

\[ {}y^{\prime \prime }-y^{\prime } = x \,{\mathrm e}^{2 x} \sin \left (x \right ) \]

[[_2nd_order, _missing_y]]

3220

\[ {}y^{\prime \prime }+2 y^{\prime } = x^{2} {\mathrm e}^{-x} \sin \left (x \right ) \]

[[_2nd_order, _missing_y]]

3228

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 1-x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

3244

\[ {}y^{\prime \prime } = \cos \left (t \right ) \]

[[_2nd_order, _quadrature]]

3249

\[ {}x y^{\prime \prime } = x^{2}+1 \]

[[_2nd_order, _quadrature]]

3250

\[ {}\left (1-x \right ) y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_y]]

3251

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (y^{\prime }+1\right ) = 0 \]

[[_2nd_order, _missing_y]]

3253

\[ {}x y^{\prime \prime }+x = y^{\prime } \]

[[_2nd_order, _missing_y]]

3272

\[ {}y^{\prime \prime } = \sec \left (x \right ) \tan \left (x \right ) \]
i.c.

[[_2nd_order, _quadrature]]

3284

\[ {}\left (1-{\mathrm e}^{x}\right ) y^{\prime \prime } = {\mathrm e}^{x} y^{\prime } \]
i.c.

[[_2nd_order, _missing_y]]

3494

\[ {}\left (x +1\right )^{2} y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }+y = x^{2} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

3565

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

3575

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

3584

\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \]

[[_2nd_order, _quadrature]]

3585

\[ {}y^{\prime \prime } = x^{n} \]

[[_2nd_order, _quadrature]]

3587

\[ {}y^{\prime \prime } = \cos \left (x \right ) \]
i.c.

[[_2nd_order, _quadrature]]

3589

\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \]
i.c.

[[_2nd_order, _quadrature]]

3699

\[ {}y^{\prime \prime }+4 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

3708

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

3773

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

3774

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \cos \left (x \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

4124

\[ {}2 y^{\prime \prime }+3 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

4127

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

4426

\[ {}x y^{\prime \prime } = y^{\prime }+x \]

[[_2nd_order, _missing_y]]

4484

\[ {}y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} \left (x^{2}+10\right ) \]

[[_2nd_order, _missing_y]]

4508

\[ {}y^{\prime \prime }+y^{\prime } = \frac {1}{{\mathrm e}^{x}+1} \]

[[_2nd_order, _missing_y]]

5916

\[ {}y^{\prime \prime }+2 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

5945

\[ {}y^{\prime \prime } = 0 \]
i.c.

[[_2nd_order, _quadrature]]

5958

\[ {}y^{\prime \prime }-3 y^{\prime } = 2 \,{\mathrm e}^{2 x} \sin \left (x \right ) \]

[[_2nd_order, _missing_y]]

5959

\[ {}y^{\prime \prime }+y^{\prime } = x^{2}+2 x \]

[[_2nd_order, _missing_y]]

5960

\[ {}y^{\prime \prime }+y^{\prime } = x +\sin \left (2 x \right ) \]

[[_2nd_order, _missing_y]]

5991

\[ {}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = \ln \left (x \right ) x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

5993

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} {\mathrm e}^{-x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

5994

\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

5999

\[ {}x y^{\prime \prime }-y^{\prime } = x^{2} \]

[[_2nd_order, _missing_y]]

6009

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (y^{\prime }+1\right ) = 0 \]

[[_2nd_order, _missing_y]]

6015

\[ {}x y^{\prime \prime }-y^{\prime } = x^{2} \]
i.c.

[[_2nd_order, _missing_y]]

6137

\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

6142

\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

6151

\[ {}y^{\prime \prime }-4 y^{\prime } = 10 \]

[[_2nd_order, _missing_x]]

6172

\[ {}2 y^{\prime \prime }+y^{\prime } = 2 x \]

[[_2nd_order, _missing_y]]

6182

\[ {}y^{\prime \prime }-2 y^{\prime } = 9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _missing_y]]

6197

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x -\frac {1}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

6219

\[ {}x y^{\prime \prime }+y^{\prime } = 4 x \]

[[_2nd_order, _missing_y]]

6408

\[ {}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-2 x \right ) y^{\prime }-2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

6513

\[ {}y^{\prime \prime } = 9 x^{2}+2 x -1 \]

[[_2nd_order, _quadrature]]

6539

\[ {}y^{\prime \prime }-7 y^{\prime } = -3 \]

[[_2nd_order, _missing_x]]

6540

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = \ln \left (x \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

6712

\[ {}y^{\prime \prime }-4 y^{\prime } = 5 \]

[[_2nd_order, _missing_x]]

6753

\[ {}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y = \ln \left (x +1\right )^{2}+x -1 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

6754

\[ {}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y = 6 x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

6773

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {2}{x^{3}} \]

[[_2nd_order, _missing_y]]

6774

\[ {}x y^{\prime \prime }-y^{\prime } = -\frac {2}{x}-\ln \left (x \right ) \]

[[_2nd_order, _missing_y]]

6910

\[ {}x y^{\prime \prime }+2 y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

6927

\[ {}y^{\prime \prime } = f \left (x \right ) \]

[[_2nd_order, _quadrature]]

6987

\[ {}x y^{\prime \prime }-y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

6988

\[ {}y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_x]]

7479

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

7484

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

7490

\[ {}y^{\prime \prime }+x y^{\prime }+y = 2 x \,{\mathrm e}^{x}-1 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

7492

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

7494

\[ {}x \left (x +1\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }-y = x +\frac {1}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

7581

\[ {}y^{\prime \prime } = 2+x \]

[[_2nd_order, _quadrature]]

7589

\[ {}y^{\prime \prime } = 3 x +1 \]

[[_2nd_order, _quadrature]]

7615

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

7674

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

7675

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

7676

\[ {}\left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

7759

\[ {}y^{\prime \prime }+y^{\prime } = 1 \]

[[_2nd_order, _missing_x]]

7764

\[ {}x y^{\prime \prime }-2 y^{\prime } = x^{3} \]

[[_2nd_order, _missing_y]]

7911

\[ {}x y^{\prime \prime }+y^{\prime } = 4 x \]

[[_2nd_order, _missing_y]]

7936

\[ {}x y^{\prime \prime }-3 y^{\prime } = 5 x \]

[[_2nd_order, _missing_y]]

7977

\[ {}y^{\prime \prime }-2 y^{\prime } = 12 x -10 \]

[[_2nd_order, _missing_y]]

7980

\[ {}y^{\prime \prime }+y^{\prime } = 10 x^{4}+2 \]

[[_2nd_order, _missing_y]]

8053

\[ {}y^{\prime \prime } = \tan \left (x \right ) \]
i.c.

[[_2nd_order, _quadrature]]

8054

\[ {}y^{\prime \prime }-2 y^{\prime } = \ln \left (x \right ) \]
i.c.

[[_2nd_order, _missing_y]]

8061

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {2}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

8223

\[ {}y^{\prime \prime }-y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

8225

\[ {}y^{\prime \prime }+2 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

8362

\[ {}t y^{\prime \prime }-y^{\prime } = 2 t^{2} \]
i.c.

[[_2nd_order, _missing_y]]

8496

\[ {}x y^{\prime \prime } = y^{\prime }+x^{5} \]
i.c.

[[_2nd_order, _missing_y]]

8497

\[ {}x y^{\prime \prime }+y^{\prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_y]]

8759

\[ {}t y^{\prime \prime }+4 y^{\prime } = t^{2} \]

[[_2nd_order, _missing_y]]

8760

\[ {}\left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_y]]

8762

\[ {}t y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

8766

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

8767

\[ {}y^{\prime \prime } = 1 \]

[[_2nd_order, _quadrature]]

8768

\[ {}y^{\prime \prime } = f \left (t \right ) \]

[[_2nd_order, _quadrature]]

8769

\[ {}y^{\prime \prime } = k \]

[[_2nd_order, _quadrature]]

8772

\[ {}y^{\prime \prime } = 4 \sin \left (x \right )-4 \]

[[_2nd_order, _quadrature]]

9072

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

9075

\[ {}a y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

9078

\[ {}y^{\prime \prime } = 1 \]

[[_2nd_order, _quadrature]]

9080

\[ {}y^{\prime \prime } = x \]

[[_2nd_order, _quadrature]]

9083

\[ {}y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

9086

\[ {}y^{\prime \prime }+y^{\prime } = 1 \]

[[_2nd_order, _missing_x]]

9089

\[ {}y^{\prime \prime }+y^{\prime } = x \]

[[_2nd_order, _missing_y]]

9102

\[ {}y^{\prime \prime }+y^{\prime } = 1 \]

[[_2nd_order, _missing_x]]

9103

\[ {}y^{\prime \prime }+y^{\prime } = x \]

[[_2nd_order, _missing_y]]

9104

\[ {}y^{\prime \prime }+y^{\prime } = x +1 \]

[[_2nd_order, _missing_y]]

9105

\[ {}y^{\prime \prime }+y^{\prime } = x^{2}+x +1 \]

[[_2nd_order, _missing_y]]

9106

\[ {}y^{\prime \prime }+y^{\prime } = x^{3}+x^{2}+x +1 \]

[[_2nd_order, _missing_y]]

9107

\[ {}y^{\prime \prime }+y^{\prime } = \sin \left (x \right ) \]

[[_2nd_order, _missing_y]]

9108

\[ {}y^{\prime \prime }+y^{\prime } = \cos \left (x \right ) \]

[[_2nd_order, _missing_y]]

10997

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

11030

\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11075

\[ {}x y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

11091

\[ {}x y^{\prime \prime }-x y^{\prime }-y-x \left (x +1\right ) {\mathrm e}^{x} = 0 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

11141

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y-a \,x^{2} = 0 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

11147

\[ {}x^{2} y^{\prime \prime }+\left (x +a \right ) y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11150

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

11157

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y-x \sin \left (x \right )-\left (a \,x^{2}+12 a +4\right ) \cos \left (x \right ) = 0 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

11163

\[ {}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11165

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y-x^{2} \ln \left (x \right ) = 0 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

11210

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-2 \cos \left (x \right )+2 x = 0 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

11211

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+a x y^{\prime }+\left (a -2\right ) y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11217

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

11218

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-a = 0 \]

[[_2nd_order, _missing_y]]

11226

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 \left (v -1\right ) x y^{\prime }-2 v y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11233

\[ {}x \left (x +1\right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11235

\[ {}x \left (-1+x \right ) y^{\prime \prime }+a y^{\prime }-2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11243

\[ {}x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{{7}/{3}} = 0 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

11246

\[ {}\left (-2+x \right )^{2} y^{\prime \prime }-\left (-2+x \right ) y^{\prime }-3 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11247

\[ {}2 x^{2} y^{\prime \prime }-\left (2 x^{2}+l -5 x \right ) y^{\prime }-\left (4 x -1\right ) y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11264

\[ {}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y-3 x -1 = 0 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

11266

\[ {}\left (3 x -1\right )^{2} y^{\prime \prime }+3 \left (3 x -1\right ) y^{\prime }-9 y-\ln \left (3 x -1\right )^{2} = 0 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

11278

\[ {}\left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

11280

\[ {}\left (a \,x^{2}+b x \right ) y^{\prime \prime }+2 b y^{\prime }-2 a y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11291

\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+2 \left (x^{2}-1\right ) y^{\prime }-2 x y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11298

\[ {}x \left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime }-6 x y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11408

\[ {}y^{\prime \prime } = -\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}+\frac {y}{\sin \left (x \right )^{2}} \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

12446

\[ {}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+a y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

12477

\[ {}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a n \,x^{n -1}+b m \,x^{m -1}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

12490

\[ {}x y^{\prime \prime }+a x y^{\prime }+a y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

12503

\[ {}x y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (2 a x +b \right ) y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

12508

\[ {}x y^{\prime \prime }+x \left (a \,x^{2}+b \right ) y^{\prime }+\left (3 a \,x^{2}+b \right ) y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

12515

\[ {}x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+a n \,x^{n -1} y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

12526

\[ {}\left (x +a \right ) y^{\prime \prime }+\left (b x +c \right ) y^{\prime }+b y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

12530

\[ {}\left (x +\gamma \right ) y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (a n \,x^{n -1}+b m \,x^{m -1}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

12584

\[ {}\left (x^{2}+a \right ) y^{\prime \prime }+2 b x y^{\prime }+2 \left (b -1\right ) y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

12596

\[ {}\left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (d x +k \right ) y^{\prime }+\left (d -2 a \right ) y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

12610

\[ {}x \left (a \,x^{2}+b \right ) y^{\prime \prime }+2 \left (a \,x^{2}+b \right ) y^{\prime }-2 y a x = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

12671

\[ {}\left (a \,x^{n}+b x +c \right ) y^{\prime \prime } = a n \left (n -1\right ) x^{n -2} y \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

12717

\[ {}y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a \lambda \,{\mathrm e}^{\lambda x}+b \mu \,{\mathrm e}^{\mu x}\right ) y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

12867

\[ {}y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{2 x}+1 \]

[[_2nd_order, _missing_y]]

12871

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

12912

\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \]

[[_2nd_order, _quadrature]]

12921

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

12922

\[ {}\left (-1+x \right )^{2} y^{\prime \prime }+4 \left (-1+x \right ) y^{\prime }+2 y = \cos \left (x \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

12937

\[ {}\left (x^{2}-x \right ) y^{\prime \prime }+\left (4 x +2\right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

12944

\[ {}\sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 \sin \left (x \right ) y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

12959

\[ {}x^{\prime \prime } = -3 \sqrt {t} \]
i.c.

[[_2nd_order, _quadrature]]

12964

\[ {}x^{\prime }+t x^{\prime \prime } = 1 \]
i.c.

[[_2nd_order, _missing_y]]

13017

\[ {}x^{\prime \prime }+x^{\prime } = 3 t \]

[[_2nd_order, _missing_y]]

13034

\[ {}x^{\prime \prime }-2 x^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13062

\[ {}x^{\prime \prime }-x^{\prime } = 6+{\mathrm e}^{2 t} \]

[[_2nd_order, _missing_y]]

13070

\[ {}x^{\prime \prime }-2 x^{\prime } = 4 \]
i.c.

[[_2nd_order, _missing_x]]

13077

\[ {}t^{2} x^{\prime \prime }+3 t x^{\prime }+x = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

13087

\[ {}t^{2} x^{\prime \prime }-2 x = t^{3} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13170

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

13449

\[ {}\left (2 x +1\right ) \left (x +1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = \left (2 x +1\right )^{2} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13467

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13473

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

13474

\[ {}x^{2} y^{\prime \prime }-2 y = 4 x -8 \]
i.c.

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13479

\[ {}\left (2+x \right )^{2} y^{\prime \prime }-\left (2+x \right ) y^{\prime }-3 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

13675

\[ {}y^{\prime \prime }-4 y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13687

\[ {}x^{\prime \prime }-4 x^{\prime } = t^{2} \]

[[_2nd_order, _missing_y]]

13714

\[ {}t^{2} x^{\prime \prime }-2 x = t^{3} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13715

\[ {}x^{\prime \prime }-4 x^{\prime } = \tan \left (t \right ) \]

[[_2nd_order, _missing_y]]

13720

\[ {}t^{2} x^{\prime \prime }+t x^{\prime }-x = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

13722

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

13725

\[ {}3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

13914

\[ {}y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

13915

\[ {}x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

13916

\[ {}y^{\prime \prime }+2 x^{2} y^{\prime }+4 x y = 2 x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13917

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 1-2 x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13920

\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 2 x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13922

\[ {}x y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

13923

\[ {}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = \cos \left (x \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13924

\[ {}y^{\prime \prime }+\cot \left (x \right ) y^{\prime }-\csc \left (x \right )^{2} y = \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13925

\[ {}x \ln \left (x \right ) y^{\prime \prime }+2 y^{\prime }-\frac {y}{x} = 1 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

14008

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = t^{7} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

14151

\[ {}x y^{\prime \prime }-y^{\prime } = x^{2} {\mathrm e}^{x} \]
i.c.

[[_2nd_order, _missing_y]]

14182

\[ {}y^{\prime \prime }-3 y^{\prime } = 2-6 x \]

[[_2nd_order, _missing_y]]

14231

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

14233

\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

14235

\[ {}x^{2} y^{\prime \prime }-2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

14249

\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

14848

\[ {}y^{\prime \prime }+2 y^{\prime } = 3 t +2 \]
i.c.

[[_2nd_order, _missing_y]]

14849

\[ {}y^{\prime \prime }+4 y^{\prime } = 3 t +2 \]
i.c.

[[_2nd_order, _missing_y]]

14905

\[ {}y^{\prime \prime } = \frac {x +1}{-1+x} \]

[[_2nd_order, _quadrature]]

14919

\[ {}y^{\prime \prime } = \sin \left (2 x \right ) \]

[[_2nd_order, _quadrature]]

14920

\[ {}y^{\prime \prime }-3 = x \]

[[_2nd_order, _quadrature]]

14928

\[ {}x y^{\prime \prime }+2 = \sqrt {x} \]
i.c.

[[_2nd_order, _quadrature]]

15130

\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]

[[_2nd_order, _missing_y]]

15131

\[ {}x y^{\prime \prime } = 2 y^{\prime } \]

[[_2nd_order, _missing_y]]

15132

\[ {}y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_x]]

15133

\[ {}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _missing_y]]

15135

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

15142

\[ {}y^{\prime \prime } = 2 y^{\prime }-6 \]

[[_2nd_order, _missing_x]]

15144

\[ {}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x} \]

[[_2nd_order, _missing_y]]

15152

\[ {}y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_x]]

15158

\[ {}x y^{\prime \prime }-y^{\prime } = 6 x^{5} \]

[[_2nd_order, _missing_y]]

15162

\[ {}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x} \]

[[_2nd_order, _missing_y]]

15164

\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]
i.c.

[[_2nd_order, _missing_y]]

15165

\[ {}x y^{\prime \prime } = 2 y^{\prime } \]
i.c.

[[_2nd_order, _missing_y]]

15166

\[ {}y^{\prime \prime } = y^{\prime } \]
i.c.

[[_2nd_order, _missing_x]]

15167

\[ {}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _missing_y]]

15170

\[ {}x y^{\prime \prime }+2 y^{\prime } = 6 \]
i.c.

[[_2nd_order, _missing_y]]

15233

\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15239

\[ {}y^{\prime \prime }+3 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

15301

\[ {}x^{2} y^{\prime \prime }-2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

15312

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

15356

\[ {}y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{\frac {x}{2}} \]

[[_2nd_order, _missing_y]]

15360

\[ {}y^{\prime \prime }+3 y^{\prime } = 26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right ) \]

[[_2nd_order, _missing_y]]

15371

\[ {}y^{\prime \prime } = 6 x \,{\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _quadrature]]

15376

\[ {}y^{\prime \prime }+4 y^{\prime } = 20 \]

[[_2nd_order, _missing_x]]

15377

\[ {}y^{\prime \prime }+4 y^{\prime } = x^{2} \]

[[_2nd_order, _missing_y]]

15428

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 85 \cos \left (2 \ln \left (x \right )\right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15429

\[ {}x^{2} y^{\prime \prime }-2 y = 15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15431

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = \frac {10}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15440

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = \sqrt {x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15444

\[ {}x^{2} y^{\prime \prime }-2 y = \frac {1}{-2+x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15446

\[ {}x y^{\prime \prime }+\left (2+2 x \right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15448

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = \frac {10}{x} \]
i.c.

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15462

\[ {}2 x y^{\prime \prime }+y^{\prime } = \sqrt {x} \]

[[_2nd_order, _missing_y]]

15482

\[ {}2 y^{\prime \prime }-7 y^{\prime }+3 = 0 \]

[[_2nd_order, _missing_x]]

15484

\[ {}x y^{\prime \prime } = 3 y^{\prime } \]

[[_2nd_order, _missing_y]]

15485

\[ {}y^{\prime \prime }-5 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

15499

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = \frac {1}{x^{2}+1} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15504

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (x +1\right )^{2}} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15505

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15715

\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

15922

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}} = \frac {1}{t} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

16110

\[ {}t^{2} y^{\prime \prime }+t y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

16127

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

16129

\[ {}y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

16142

\[ {}y^{\prime \prime }-y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16143

\[ {}3 y^{\prime \prime }-y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16177

\[ {}y^{\prime \prime }+2 y^{\prime } = 3-4 t \]

[[_2nd_order, _missing_y]]

16182

\[ {}y^{\prime \prime } = 3 t^{4}-2 t \]

[[_2nd_order, _quadrature]]

16192

\[ {}y^{\prime \prime }-2 y^{\prime } = 52 \sin \left (3 t \right ) \]

[[_2nd_order, _missing_y]]

16200

\[ {}y^{\prime \prime }+4 y^{\prime } = 8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t} \]

[[_2nd_order, _missing_y]]

16201

\[ {}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t} \]

[[_2nd_order, _missing_y]]

16202

\[ {}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \]

[[_2nd_order, _missing_y]]

16203

\[ {}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t} \]

[[_2nd_order, _missing_y]]

16204

\[ {}y^{\prime \prime } = t^{2}+{\mathrm e}^{t}+\sin \left (t \right ) \]

[[_2nd_order, _quadrature]]

16205

\[ {}y^{\prime \prime }+3 y^{\prime } = 18 \]
i.c.

[[_2nd_order, _missing_x]]

16213

\[ {}y^{\prime \prime }-3 y^{\prime } = -{\mathrm e}^{3 t}-2 t \]
i.c.

[[_2nd_order, _missing_y]]

16214

\[ {}y^{\prime \prime }-y^{\prime } = -3 t -4 t^{2} {\mathrm e}^{2 t} \]
i.c.

[[_2nd_order, _missing_y]]

16215

\[ {}y^{\prime \prime }-2 y^{\prime } = 2 t^{2} \]
i.c.

[[_2nd_order, _missing_y]]

16216

\[ {}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \]
i.c.

[[_2nd_order, _missing_y]]

16217

\[ {}y^{\prime \prime }-3 y^{\prime } = {\mathrm e}^{-3 t}-{\mathrm e}^{3 t} \]
i.c.

[[_2nd_order, _missing_y]]

16230

\[ {}y^{\prime \prime }+16 y^{\prime } = t \]

[[_2nd_order, _missing_y]]

16275

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = \ln \left (t \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

16277

\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 2 \ln \left (t \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

16399

\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x^{2}} \]
i.c.

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

16400

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \ln \left (x \right ) \]
i.c.

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

16404

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

16417

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

16497

\[ {}y^{\prime \prime }+5 y^{\prime } = 5 t^{2} \]

[[_2nd_order, _missing_y]]

16498

\[ {}y^{\prime \prime }-4 y^{\prime } = -3 \sin \left (t \right ) \]

[[_2nd_order, _missing_y]]

16501

\[ {}y^{\prime \prime }-2 y^{\prime } = \frac {1}{1+{\mathrm e}^{2 t}} \]

[[_2nd_order, _missing_y]]

16531

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

16830

\[ {}\left (-1+x \right ) y^{\prime \prime } = 1 \]

[[_2nd_order, _quadrature]]

16839

\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \]
i.c.

[[_2nd_order, _quadrature]]

16840

\[ {}y^{\prime \prime } = 2 \ln \left (x \right ) x \]

[[_2nd_order, _quadrature]]

16841

\[ {}x y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_y]]

16842

\[ {}x y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

16844

\[ {}x y^{\prime \prime } = y^{\prime }+x^{2} \]

[[_2nd_order, _missing_y]]

16856

\[ {}y^{\prime \prime }+y^{\prime }+2 = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16895

\[ {}y^{\prime \prime }+3 y^{\prime } = 3 \]

[[_2nd_order, _missing_x]]

16896

\[ {}y^{\prime \prime }-7 y^{\prime } = \left (-1+x \right )^{2} \]

[[_2nd_order, _missing_y]]

16897

\[ {}y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{x} \]

[[_2nd_order, _missing_y]]

16898

\[ {}y^{\prime \prime }+7 y^{\prime } = {\mathrm e}^{-7 x} \]

[[_2nd_order, _missing_y]]

16901

\[ {}4 y^{\prime \prime }-3 y^{\prime } = x \,{\mathrm e}^{\frac {3 x}{4}} \]

[[_2nd_order, _missing_y]]

16902

\[ {}y^{\prime \prime }-4 y^{\prime } = x \,{\mathrm e}^{4 x} \]

[[_2nd_order, _missing_y]]

16932

\[ {}y^{\prime \prime }+2 y^{\prime } = -2 \]

[[_2nd_order, _missing_x]]

16940

\[ {}y^{\prime \prime }+8 y^{\prime } = 8 x \]

[[_2nd_order, _missing_y]]

16944

\[ {}7 y^{\prime \prime }-y^{\prime } = 14 x \]

[[_2nd_order, _missing_y]]

16945

\[ {}y^{\prime \prime }+3 y^{\prime } = 3 x \,{\mathrm e}^{-3 x} \]

[[_2nd_order, _missing_y]]

16954

\[ {}y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _missing_y]]

16955

\[ {}y^{\prime \prime }+2 y^{\prime } = 4 \,{\mathrm e}^{x} \left (\sin \left (x \right )+\cos \left (x \right )\right ) \]

[[_2nd_order, _missing_y]]

16957

\[ {}4 y^{\prime \prime }+8 y^{\prime } = x \sin \left (x \right ) \]

[[_2nd_order, _missing_y]]

16972

\[ {}y^{\prime \prime }+4 y^{\prime } = x +{\mathrm e}^{-4 x} \]

[[_2nd_order, _missing_y]]

16978

\[ {}y^{\prime \prime }-4 y^{\prime } = 2 \cos \left (4 x \right )^{2} \]

[[_2nd_order, _missing_y]]

16980

\[ {}y^{\prime \prime }-3 y^{\prime } = 18 x -10 \cos \left (x \right ) \]

[[_2nd_order, _missing_y]]

16987

\[ {}y^{\prime \prime }+y^{\prime } = \cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2} \]

[[_2nd_order, _missing_y]]

16990

\[ {}y^{\prime \prime }+y^{\prime } = x^{2}-{\mathrm e}^{-x}+{\mathrm e}^{x} \]

[[_2nd_order, _missing_y]]

16997

\[ {}y^{\prime \prime }-3 y^{\prime } = 1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right ) \]

[[_2nd_order, _missing_y]]

17003

\[ {}y^{\prime \prime }+2 y^{\prime }+1 = 3 \sin \left (2 x \right )+\cos \left (x \right ) \]

[[_2nd_order, _missing_y]]

17015

\[ {}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x} \]
i.c.

[[_2nd_order, _missing_y]]

17022

\[ {}y^{\prime \prime }-y^{\prime } = -5 \,{\mathrm e}^{-x} \left (\sin \left (x \right )+\cos \left (x \right )\right ) \]
i.c.

[[_2nd_order, _missing_y]]

17038

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

17039

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

17041

\[ {}x y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

17049

\[ {}x^{2} y^{\prime \prime }-2 y = \sin \left (\ln \left (x \right )\right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

17050

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = -\frac {16 \ln \left (x \right )}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

17052

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

17053

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 \ln \left (x \right )^{2}+12 x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

17070

\[ {}y^{\prime \prime }+y^{\prime } = \frac {1}{{\mathrm e}^{x}+1} \]

[[_2nd_order, _missing_y]]

17076

\[ {}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right ) \]

[[_2nd_order, _missing_y]]

17085

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {1}{x^{2}+1} \]
i.c.

[[_2nd_order, _missing_y]]

17109

\[ {}y^{\prime \prime }+\alpha y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17116

\[ {}x y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

17486

\[ {}t^{2} y^{\prime \prime }-2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

17516

\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

17549

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

17551

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }-6 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

17552

\[ {}x^{2} y^{\prime \prime }-2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

17556

\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-3 y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

17566

\[ {}y^{\prime \prime }+2 y^{\prime } = 3+4 \sin \left (2 t \right ) \]

[[_2nd_order, _missing_y]]

17584

\[ {}y^{\prime \prime }+3 y^{\prime } = 2 t^{4}+t^{2} {\mathrm e}^{-3 t}+\sin \left (3 t \right ) \]

[[_2nd_order, _missing_y]]

17594

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

17626

\[ {}t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

17629

\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

17814

\[ {}y^{\prime \prime } = \sin \left (x \right ) \]

[[_2nd_order, _quadrature]]

17950

\[ {}x^{2} y^{\prime \prime }-2 y = x^{2}+\frac {1}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18114

\[ {}x y^{\prime \prime }+y^{\prime } = 4 x \]

[[_2nd_order, _missing_y]]

18170

\[ {}x y^{\prime \prime }-y^{\prime } = 3 x^{2} \]

[[_2nd_order, _missing_y]]

18171

\[ {}x y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

18174

\[ {}y^{\prime \prime }-2 y^{\prime } = 6 \]

[[_2nd_order, _missing_x]]

18176

\[ {}y^{\prime \prime } = {\mathrm e}^{x} \]

[[_2nd_order, _quadrature]]

18177

\[ {}y^{\prime \prime }-2 y^{\prime } = 4 \]

[[_2nd_order, _missing_x]]

18180

\[ {}y^{\prime \prime }+2 y^{\prime } = 6 \,{\mathrm e}^{x} \]

[[_2nd_order, _missing_y]]

18181

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

18187

\[ {}x^{2} y^{\prime \prime }-2 y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

18190

\[ {}y^{\prime \prime }+y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18217

\[ {}y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

18251

\[ {}y^{\prime \prime }-2 y^{\prime } = 12 x -10 \]

[[_2nd_order, _missing_y]]

18254

\[ {}y^{\prime \prime }+y^{\prime } = 10 x^{4}+2 \]

[[_2nd_order, _missing_y]]

18335

\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

18441

\[ {}x^{\prime \prime }+3 x^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

18516

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18599

\[ {}e y^{\prime \prime } = \frac {P \left (\frac {L}{2}-x \right )}{2} \]

[[_2nd_order, _quadrature]]

18600

\[ {}e y^{\prime \prime } = \frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2} \]

[[_2nd_order, _quadrature]]

18601

\[ {}e y^{\prime \prime } = -\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2} \]

[[_2nd_order, _quadrature]]

18602

\[ {}e y^{\prime \prime } = -P \left (L -x \right ) \]

[[_2nd_order, _quadrature]]

18603

\[ {}e y^{\prime \prime } = -P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2} \]

[[_2nd_order, _quadrature]]

18610

\[ {}x y^{\prime \prime }+2 y^{\prime } = 2 x \]

[[_2nd_order, _missing_y]]

18612

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 2 x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18613

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18614

\[ {}y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+\csc \left (x \right )^{2} y = \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18615

\[ {}\left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

18616

\[ {}\left (3 x^{2}+x \right ) y^{\prime \prime }+2 \left (1+6 x \right ) y^{\prime }+6 y = \sin \left (x \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18619

\[ {}y^{\prime \prime } = \cos \left (x \right ) \]

[[_2nd_order, _quadrature]]

18626

\[ {}x y^{\prime \prime }+3 y^{\prime } = 3 x \]

[[_2nd_order, _missing_y]]

18627

\[ {}x = y^{\prime \prime }+y^{\prime } \]

[[_2nd_order, _missing_y]]

18645

\[ {}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

18848

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = x^{4} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18851

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18855

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = {\mathrm e}^{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18861

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18865

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18870

\[ {}x y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

18871

\[ {}y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x} = x^{2} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18877

\[ {}y^{\prime \prime } = x^{2} \sin \left (x \right ) \]

[[_2nd_order, _quadrature]]

18895

\[ {}x y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

18912

\[ {}\sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 y \sin \left (x \right ) = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

18914

\[ {}y^{\prime \prime } = \frac {a}{x} \]

[[_2nd_order, _quadrature]]

18917

\[ {}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x} \]

[[_2nd_order, _missing_y]]

18920

\[ {}a y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_x]]

18924

\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = {\mathrm e}^{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18927

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

18941

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

19247

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19250

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = x^{4} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19251

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19253

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime } = \ln \left (x \right ) \]

[[_2nd_order, _missing_y]]

19254

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = {\mathrm e}^{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19268

\[ {}x y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

19269

\[ {}y^{\prime \prime }+{\mathrm e}^{x} \left (y^{\prime }+y\right ) = {\mathrm e}^{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19270

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

19273

\[ {}y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x} = x^{2} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19274

\[ {}\left (x^{2}-x \right ) y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

19275

\[ {}\left (x^{2}-x \right ) y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }-4 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

19276

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 2 x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19277

\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+\left (6 x +3\right ) y^{\prime }+2 y = \left (x +1\right ) {\mathrm e}^{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19279

\[ {}\left (-b \,x^{2}+a x \right ) y^{\prime \prime }+2 a y^{\prime }+2 b y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

19280

\[ {}\sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 y \sin \left (x \right ) = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

19287

\[ {}y^{\prime \prime } = x +\sin \left (x \right ) \]

[[_2nd_order, _quadrature]]

19288

\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \]

[[_2nd_order, _quadrature]]

19291

\[ {}y^{\prime \prime } = \frac {a}{x} \]

[[_2nd_order, _quadrature]]

19303

\[ {}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x} \]

[[_2nd_order, _missing_y]]

19312

\[ {}x y^{\prime \prime }+y^{\prime } = x \]

[[_2nd_order, _missing_y]]

19321

\[ {}a y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_x]]

19348

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

19358

\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime } = y+{\mathrm e}^{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19411

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 8 x^{3} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19417

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

19500

\[ {}x^{2} y^{\prime \prime }-2 y = x^{2}+\frac {1}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19506

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19524

\[ {}y^{\prime \prime } = x^{2} \sin \left (x \right ) \]

[[_2nd_order, _quadrature]]

19525

\[ {}y^{\prime \prime } = \sec \left (x \right )^{2} \]

[[_2nd_order, _quadrature]]

19531

\[ {}x y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

19556

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} {\mathrm e}^{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]