4.27.14 Problems 1301 to 1400

Table 4.1187: Second order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

Sympy

15400

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x} \]

15401

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

15402

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right ) \]

15403

\[ {} y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{4 x} \sin \left (2 x \right ) \]

15404

\[ {} y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{2 x} \sin \left (4 x \right ) \]

15405

\[ {} y^{\prime \prime }-4 y^{\prime }+20 y = x^{3} \sin \left (4 x \right ) \]

15406

\[ {} y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{2} {\mathrm e}^{5 x} \]

15407

\[ {} y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{4} \]

15422

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right ) \]

15423

\[ {} y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right )+3 \sin \left (3 x \right ) \]

15424

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

15425

\[ {} y^{\prime \prime }-4 y^{\prime }+5 y = 20 \sinh \left (x \right ) \]

15435

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

15436

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

15437

\[ {} y^{\prime \prime }-7 y^{\prime }+10 y = 6 \,{\mathrm e}^{3 x} \]

15438

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = \left (24 x^{2}+2\right ) {\mathrm e}^{2 x} \]

15439

\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}+1} \]

15449

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

15482

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

15486

\[ {} y^{\prime \prime }-9 y^{\prime }+14 y = 98 x^{2} \]

15487

\[ {} y^{\prime \prime }-12 y^{\prime }+36 y = 25 \sin \left (3 x \right ) \]

15488

\[ {} y^{\prime \prime }-9 y^{\prime }+14 y = 576 x^{2} {\mathrm e}^{-x} \]

15489

\[ {} y^{\prime \prime }-12 y^{\prime }+36 y = 81 \,{\mathrm e}^{3 x} \]

15491

\[ {} y^{\prime \prime }-12 y^{\prime }+36 y = 3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x} \]

15492

\[ {} y^{\prime \prime }+36 y = 6 \sec \left (6 x \right ) \]

15494

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 10 \,{\mathrm e}^{-3 x} \]

15496

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 2 \cos \left (2 x \right ) \]

15500

\[ {} 4 y^{\prime \prime }-12 y^{\prime }+9 y = x \,{\mathrm e}^{\frac {3 x}{2}} \]

15501

\[ {} 3 y^{\prime \prime }+8 y^{\prime }-3 y = 123 x \sin \left (3 x \right ) \]

15509

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

15510

\[ {} y^{\prime \prime }+4 y = 20 \,{\mathrm e}^{4 t} \]

15511

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

15512

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

15513

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{4 t} \]

15514

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = t^{2} {\mathrm e}^{4 t} \]

15515

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 7 \]

15516

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right ) \]

15517

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = 4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right ) \]

15521

\[ {} y^{\prime \prime }+9 y = 27 t^{3} \]

15522

\[ {} y^{\prime \prime }+8 y^{\prime }+7 y = 165 \,{\mathrm e}^{4 t} \]

15524

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = t^{2} {\mathrm e}^{3 t} \]

15527

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

15528

\[ {} y^{\prime \prime }-4 y^{\prime }+40 y = 122 \,{\mathrm e}^{-3 t} \]

15529

\[ {} y^{\prime \prime }-9 y = 24 \,{\mathrm e}^{-3 t} \]

15530

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right ) \]

15531

\[ {} y^{\prime \prime }+4 y = 1 \]

15532

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

15533

\[ {} y^{\prime \prime }+4 y = {\mathrm e}^{3 t} \]

15534

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

15535

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

15536

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 1 \]

15537

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = t \]

15538

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t} \]

15539

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \]

15540

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{t} \]

15543

\[ {} y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right ) \]

15544

\[ {} y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right ) \]

15545

\[ {} y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -10\right ) \]

15547

\[ {} y^{\prime \prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \]

15548

\[ {} y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \]

15551

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

15552

\[ {} y^{\prime \prime } = \delta \left (t -1\right )-\delta \left (t -4\right ) \]

15554

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

15555

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

15557

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

15558

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

15559

\[ {} y^{\prime \prime }+16 y = \delta \left (t -2\right ) \]

15560

\[ {} y^{\prime \prime }-16 y = \delta \left (t -10\right ) \]

15561

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

15562

\[ {} y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right ) \]

15563

\[ {} y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right ) \]

15564

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (t -4\right ) \]

15565

\[ {} y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right ) \]

15702

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

15717

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

15769

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

15770

\[ {} y^{\prime \prime }-7 y^{\prime }+12 y = 2 \]

15778

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

16106

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

16172

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

16173

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

16174

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

16175

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

16176

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

16177

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

16178

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

16179

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

16180

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

16181

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

16182

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

16183

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right ) \]

16184

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

16185

\[ {} 5 y^{\prime \prime }+y^{\prime }-4 y = -3 \]

16186

\[ {} y^{\prime \prime }-2 y^{\prime }-8 y = 32 t \]

16187

\[ {} 16 y^{\prime \prime }-8 y^{\prime }-15 y = 75 t \]

16188

\[ {} y^{\prime \prime }+2 y^{\prime }+26 y = -338 t \]

16189

\[ {} y^{\prime \prime }+3 y^{\prime }-4 y = -32 t^{2} \]

16190

\[ {} 8 y^{\prime \prime }+6 y^{\prime }+y = 5 t^{2} \]

16191

\[ {} y^{\prime \prime }-6 y^{\prime }+8 y = -256 t^{3} \]

16192

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