4.20.41 Problems 4001 to 4100

Table 4.1279: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

20457

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

20458

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

20459

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

20460

\[ {} y^{\prime \prime }+2 y^{\prime }-15 y = 15 x^{2} \]

20461

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

20462

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

20463

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

20464

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

20465

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

20466

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

20467

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

20468

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

20469

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

20470

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

20471

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 = 0 \]

20472

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

20473

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

20474

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

20475

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

20476

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

20477

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

20478

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

20479

\[ {} y^{\prime \prime \prime }-7 y^{\prime }-6 y = {\mathrm e}^{2 x} \left (1+x \right ) \]

20480

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

20481

\[ {} y^{\prime \prime }+4 y^{\prime }-12 y = \left (x -1\right ) {\mathrm e}^{2 x} \]

20482

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

20483

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

20484

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

20485

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

20486

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

20487

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

20488

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

20489

\[ {} y^{\left (6\right )}-2 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+3 y^{\prime \prime }-2 y^{\prime }+y = \sin \left (\frac {x}{2}\right )^{2}+{\mathrm e}^{x} \]

20490

\[ {} y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y = 16 x^{2}+256 \]

20491

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

20492

\[ {} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = 96 \sin \left (2 x \right ) \cos \left (x \right ) \]

20493

\[ {} y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y = 0 \]

20494

\[ {} y^{\prime \prime }+2 y^{\prime }+10 y+37 \sin \left (3 x \right ) = 0 \]

20495

\[ {} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime } = 24 x \cos \left (x \right ) \]

20649

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

20651

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

20652

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

20655

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

20659

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

20661

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

20667

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

20685

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

20693

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

20694

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

20695

\[ {} y^{\left (5\right )}-n^{2} y^{\prime \prime \prime } = {\mathrm e}^{a x} \]

20706

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

20707

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

20709

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

20757

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

20758

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

20759

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

20761

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

20813

\[ {} 2 y^{\prime \prime }+9 y^{\prime }-18 y = 0 \]

20814

\[ {} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y = 0 \]

20815

\[ {} y^{\prime \prime \prime }-8 y = 0 \]

20816

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

20817

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

20818

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

20819

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

20820

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

20821

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

20822

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

20823

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

20824

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

20825

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

20826

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

20827

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

20886

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

20887

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

20888

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

20895

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

20918

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

20922

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

20953

\[ {} 20 y-9 y^{\prime }+y^{\prime \prime } = 0 \]

20954

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

20955

\[ {} 8 y^{\prime \prime }+4 y^{\prime }+y = 0 \]

20956

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

20961

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

20962

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

20963

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

20964

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

20965

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

20966

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

20967

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

20968

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

20969

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

20970

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

20971

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

20972

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

20973

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

20987

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 20 \,{\mathrm e}^{-2 x} \]

20988

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

20989

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

20991

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

20992

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