4.3.84 Problems 8301 to 8400

Table 4.531: Second order ode

#

ODE

Mathematica

Maple

Sympy

23629

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

23630

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

23631

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

23632

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

23633

\[ {} 4 y^{\prime \prime }+7 y^{\prime }+3 y = 5 \cos \left (t \right ) \]

23640

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

23641

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

23642

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

23643

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

23644

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

23645

\[ {} y^{\prime \prime }+10 y^{\prime }+25 y = \frac {{\mathrm e}^{-5 x} \ln \left (x \right )}{x^{2}} \]

23646

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

23647

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

23648

\[ {} y^{\prime \prime }-12 y^{\prime }+36 y = {\mathrm e}^{6 x} \ln \left (x \right ) \]

23649

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

23650

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

23651

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

23652

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

23653

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

23654

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

23655

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

23656

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

23657

\[ {} 2 x^{2} y^{\prime \prime }+7 x y^{\prime }-3 y = \frac {\ln \left (x \right )}{x^{2}} \]

23658

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \ln \left (x \right ) \left (\frac {1}{x^{3}}+\frac {1}{x^{5}}\right ) \]

23659

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

23660

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

23661

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

23662

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

23663

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

23664

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

23665

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

23666

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

23667

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

23669

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

23670

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

23747

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

23748

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

23750

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

23751

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

23752

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

23753

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

23754

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

23756

\[ {} y^{\prime \prime }-9 y^{\prime }+18 y = 54 \]

23757

\[ {} y^{\prime \prime }-9 y = 20 \cos \left (t \right ) \]

23758

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

23759

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 24 \cosh \left (t \right ) \]

23760

\[ {} y^{\prime \prime }+10 y^{\prime }+26 y = 37 \,{\mathrm e}^{t} \]

23764

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 27 t \]

23765

\[ {} y^{\prime \prime }-y^{\prime }-6 y = \cos \left (t \right )+57 \sin \left (t \right ) \]

23766

\[ {} y^{\prime \prime }-3 y^{\prime }-4 y = 25 t \,{\mathrm e}^{-t} \]

23767

\[ {} y^{\prime \prime }+13 y^{\prime }+36 y = 10-72 t \]

23768

\[ {} y^{\prime \prime }+2 y^{\prime }-15 y = 16 t \,{\mathrm e}^{-t}-15 \]

23769

\[ {} y^{\prime \prime }-10 y^{\prime }+21 y = 21 t^{2}+t +13 \]

23770

\[ {} y^{\prime \prime }+7 y^{\prime }+10 y = 3 \,{\mathrm e}^{-2 t}-6 \,{\mathrm e}^{-5 t} \]

23771

\[ {} 4 y^{\prime \prime }-3 y^{\prime }-y = 34 \sin \left (t \right ) \]

23773

\[ {} y^{\prime \prime }+2 y^{\prime }-3 y = 3 t^{3}-9 t^{2}-5 t +1 \]

23774

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = 39 \,{\mathrm e}^{t} \sin \left (t \right ) \]

23775

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 8 \,{\mathrm e}^{t}+5 t \]

23776

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

23779

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

23780

\[ {} y^{\prime \prime }+7 y^{\prime }+6 y = 250 \,{\mathrm e}^{t} \cos \left (t \right ) \]

23781

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = 13 t +17+40 \sin \left (t \right ) \]

23869

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

23870

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

23871

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

23872

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

23873

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

23874

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

23875

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

23876

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

23877

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

23878

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

23879

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

23880

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

23962

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

23963

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

23964

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

24036

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

24037

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

24038

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

24039

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

24040

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

24041

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

24042

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

24043

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

24044

\[ {} 6 y^{\prime \prime }+11 y^{\prime }+4 y = 2 \]

24045

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

24046

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

24047

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

24070

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

24080

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

24082

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

24083

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

24089

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

24090

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

24091

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

24092

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

24093

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

24094

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

24095

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