4.5.14 Problems 1301 to 1400

Table 4.517: Second ODE non-homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

12856

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

12858

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

12859

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

12860

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

12861

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

12862

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

12863

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

12867

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

12871

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

12872

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

12873

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = \cos \left (x \right )-{\mathrm e}^{2 x} \]

12875

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

12880

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

12881

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

12883

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

12886

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

12887

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

12889

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

12890

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

12893

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

12894

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

12897

\[ {} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y = \frac {1}{x^{2}} \]

12898

\[ {} x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-8 x^{3} y = 4 x^{3} {\mathrm e}^{-x^{2}} \]

12906

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

12909

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

12911

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

12912

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

12913

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

12915

\[ {} y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0 \]

12921

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

12922

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

12933

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

12934

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

12940

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

12941

\[ {} y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \]

12942

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

12959

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

12964

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

12993

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

13017

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

13049

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

13050

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

13051

\[ {} x^{\prime \prime }+x^{\prime }+x = 12 \]

13052

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

13053

\[ {} x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (7 t \right ) \]

13054

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

13055

\[ {} x^{\prime \prime }+x^{\prime }+x = t \,{\mathrm e}^{-t} \sin \left (\pi t \right ) \]

13056

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

13057

\[ {} x^{\prime \prime }+x^{\prime }+x = 4 t +5 \,{\mathrm e}^{-t} \]

13058

\[ {} x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (2 t \right )+t \,{\mathrm e}^{t} \]

13059

\[ {} x^{\prime \prime }+x^{\prime }+x = t^{3}+1-4 t \cos \left (t \right ) \]

13060

\[ {} x^{\prime \prime }+x^{\prime }+x = -6+2 \,{\mathrm e}^{2 t} \sin \left (t \right ) \]

13061

\[ {} x^{\prime \prime }+7 x = t \,{\mathrm e}^{3 t} \]

13062

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

13063

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

13064

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

13065

\[ {} x^{\prime \prime }+x = 9 \,{\mathrm e}^{-t} \]

13066

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

13067

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

13068

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

13069

\[ {} x^{\prime \prime }-3 x^{\prime }-40 x = 2 \,{\mathrm e}^{-t} \]

13070

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

13071

\[ {} x^{\prime \prime }+2 x = \cos \left (\sqrt {2}\, t \right ) \]

13072

\[ {} x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x = \cos \left (2 t \right ) \]

13073

\[ {} x^{\prime \prime }+w^{2} x = \cos \left (\beta t \right ) \]

13074

\[ {} x^{\prime \prime }+3025 x = \cos \left (45 t \right ) \]

13084

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

13085

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

13086

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

13087

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

13088

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

13089

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

13090

\[ {} x^{\prime \prime }+\frac {x^{\prime }}{t} = a \]

13091

\[ {} t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7} \]

13092

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

13109

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

13111

\[ {} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x = 1-\operatorname {Heaviside}\left (t -5\right ) \]

13112

\[ {} x^{\prime \prime }+9 x = \sin \left (3 t \right ) \]

13113

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

13115

\[ {} x^{\prime \prime }+4 x = \cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \]

13118

\[ {} x^{\prime \prime }+\pi ^{2} x = \pi ^{2} \operatorname {Heaviside}\left (1-t \right ) \]

13119

\[ {} x^{\prime \prime }-4 x = 1-\operatorname {Heaviside}\left (t -1\right ) \]

13120

\[ {} x^{\prime \prime }+3 x^{\prime }+2 x = {\mathrm e}^{-4 t} \]

13122

\[ {} x^{\prime \prime }-x = \delta \left (t -5\right ) \]

13123

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

13124

\[ {} x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right ) \]

13125

\[ {} x^{\prime \prime }+x = 3 \delta \left (t -2 \pi \right ) \]

13126

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

13127

\[ {} x^{\prime \prime }+4 x = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right ) \]

13169

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

13180

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = -8 \sin \left (2 x \right ) \]

13310

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x} \]

13311

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x} \]

13326

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

13327

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 2-12 x +6 \,{\mathrm e}^{x} \]

13372

\[ {} y^{\prime \prime }-3 y^{\prime }+8 y = 4 x^{2} \]

13373

\[ {} y^{\prime \prime }-2 y^{\prime }-8 y = 4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x} \]

13374

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 6 \sin \left (2 x \right )+7 \cos \left (2 x \right ) \]

13375

\[ {} y^{\prime \prime }+2 y^{\prime }+2 y = 10 \sin \left (4 x \right ) \]

13376

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