4.19.4 Problems 301 to 400

Table 4.1185: Third and higher order non-homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

8061

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

8065

\[ {} \left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y = 8 \]

8069

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

8070

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

8071

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

8185

\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 12 x^{2} \]

8815

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

8816

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 \sin \left (t \right )-5 \cos \left (t \right ) \]

8817

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

8820

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

8825

\[ {} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \sin \left (3 x \right ) \]

8868

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

8945

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

8946

\[ {} y^{\prime \prime \prime }-8 y = {\mathrm e}^{i x} \]

8947

\[ {} y^{\prime \prime \prime \prime }+16 y = \cos \left (x \right ) \]

8948

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

8949

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

8958

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

8959

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

9270

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

9318

\[ {} y^{\prime \prime \prime \prime } = \sin \left (x \right )+24 \]

9319

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 10+42 \,{\mathrm e}^{3 x} \]

9320

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

9618

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

9619

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

10144

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

10158

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

10163

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

10465

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

12724

\[ {} y^{\prime \prime \prime }+a \,x^{3} y-b x = 0 \]

12727

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

12734

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

12735

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

12739

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

12742

\[ {} 18 \,{\mathrm e}^{x}-3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime } = 0 \]

12747

\[ {} x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-f \left (x \right ) = 0 \]

12748

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

12759

\[ {} x^{2} y^{\prime \prime \prime }+4 x y^{\prime \prime }+y^{\prime } \left (x^{2}+2\right )+3 x y-f \left (x \right ) = 0 \]

12760

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

12769

\[ {} \left (x^{2}+1\right ) y^{\prime \prime \prime }+8 x y^{\prime \prime }+10 y^{\prime }-3+\frac {1}{x^{2}}-2 \ln \left (x \right ) = 0 \]

12775

\[ {} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y-6 x^{3} \left (x -1\right ) \ln \left (x \right )+x^{3} \left (x +8\right ) = 0 \]

12781

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

12786

\[ {} 4 x^{4} y^{\prime \prime \prime }-4 x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }-1 = 0 \]

12792

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

12793

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

12798

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

12800

\[ {} y^{\prime \prime \prime \prime }-12 y^{\prime \prime }+12 y-16 x^{4} {\mathrm e}^{x^{2}} = 0 \]

12801

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

12805

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y-32 \sin \left (2 x \right )+24 \cos \left (2 x \right ) = 0 \]

12807

\[ {} 4 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+11 y^{\prime \prime }-3 y^{\prime }-4 \cos \left (x \right ) = 0 \]

12808

\[ {} y^{\prime \prime \prime \prime } x +5 y^{\prime \prime \prime }-24 = 0 \]

12811

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

12832

\[ {} \left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \,{\mathrm e}^{x} y^{\prime }+y \,{\mathrm e}^{x}-\frac {1}{x^{5}} = 0 \]

12834

\[ {} y^{\prime \prime \prime \prime } \sin \left (x \right )^{6}+4 y^{\prime \prime \prime } \sin \left (x \right )^{5} \cos \left (x \right )-6 y^{\prime \prime } \sin \left (x \right )^{6}-4 y^{\prime } \sin \left (x \right )^{5} \cos \left (x \right )+y \sin \left (x \right )^{6}-f = 0 \]

12838

\[ {} y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime }-a x -b \sin \left (x \right )-c \cos \left (x \right ) = 0 \]

12839

\[ {} y^{\left (6\right )}+y-\sin \left (\frac {3 x}{2}\right ) \sin \left (\frac {x}{2}\right ) = 0 \]

12840

\[ {} y^{\left (5\right )}-a x y-b = 0 \]

12842

\[ {} y^{\left (5\right )}+a y^{\prime \prime \prime \prime }-f = 0 \]

12845

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

13062

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

13065

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

14210

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

14212

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

14215

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

14217

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = x \]

14224

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

14225

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

14226

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

14228

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

14229

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

14230

\[ {} 2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 10 x +\frac {10}{x} \]

14234

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

14236

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

14237

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

14238

\[ {} y+3 x y^{\prime }+9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = \left (\ln \left (x \right )+1\right )^{2} \]

14239

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

14242

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

14244

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

14245

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

14270

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

14279

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

14280

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

14459

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

14462

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

14740

\[ {} y^{\prime \prime \prime }+4 y^{\prime \prime }+y^{\prime }-6 y = -18 x^{2}+1 \]

14741

\[ {} y^{\prime \prime \prime }+2 y^{\prime \prime }-3 y^{\prime }-10 y = 8 x \,{\mathrm e}^{-2 x} \]

14742

\[ {} y^{\prime \prime \prime }+y^{\prime \prime }+3 y^{\prime }-5 y = 5 \sin \left (2 x \right )+10 x^{2}+3 x +7 \]

14743

\[ {} 4 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+3 y = 3 x^{3}-8 x \]

14746

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 4 \,{\mathrm e}^{x}-18 \,{\mathrm e}^{-x} \]

14747

\[ {} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime } = 9 \,{\mathrm e}^{2 x}-8 \,{\mathrm e}^{3 x} \]

14748

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

14749

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

14750

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = x \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{4 x} \]

14751

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 3 x^{2} {\mathrm e}^{x}-7 \,{\mathrm e}^{x} \]

14754

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime } = 18 x^{2}+16 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x}-9 \]

14755

\[ {} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+7 y^{\prime \prime }-5 y^{\prime }+6 y = 5 \sin \left (x \right )-12 \sin \left (2 x \right ) \]

14770

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y = 3 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-\sin \left (x \right ) \]

14771

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }-4 y = 8 x^{2}+3-6 \,{\mathrm e}^{2 x} \]

14777

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

14778

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = x \,{\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \]