4.20.19 Problems 1801 to 1900

Table 4.939: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

9082

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

9083

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

9086

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

9089

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

9092

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

9095

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

9096

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

9097

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

9098

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

9099

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

9100

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

9101

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

9102

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

9103

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

9104

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

9105

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

9106

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

9107

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

9108

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

9109

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

9110

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

9111

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

9112

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

9113

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

9114

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

9115

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

9165

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

9564

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

9677

\[ {} y^{\prime \prime }+3 y^{\prime }+4 y = 0 \]

9959

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

9991

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

10997

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

10998

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

10999

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

11000

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

11001

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

11002

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

11003

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

11004

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

11005

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

11026

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

11027

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

11055

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

11424

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

11427

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

11428

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

11434

\[ {} y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime }+10 y = 0 \]

11435

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

11436

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

11437

\[ {} y^{\prime \prime \prime }+\operatorname {a2} y^{\prime \prime }+\operatorname {a1} y^{\prime }+\operatorname {a0} y = 0 \]

11443

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

11498

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

11499

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

11500

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

11501

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

11502

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

11503

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

11506

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

11508

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

11536

\[ {} f \left (y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y\right )+2 \operatorname {df} \left (y^{\prime \prime \prime }-a^{2} y^{\prime }\right ) = 0 \]

11537

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

11539

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

11540

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

11543

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

11545

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

11771

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

12422

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

12432

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

12840

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

12841

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]

12842

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

12843

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

12844

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

12845

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

12846

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

12847

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime } = 0 \]

12848

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

12849

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

12850

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

12851

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

12852

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

12853

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

12854

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

12855

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

12856

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

12857

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

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

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

12864

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

12865

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

12866

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

12867

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

12868

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

12873

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

12874

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

12875

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