4.2.73 Problems 7201 to 7300

Table 4.351: Second order linear ODE

#

ODE

Mathematica

Maple

Sympy

23573

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

23574

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

23576

\[ {} y^{\prime \prime }-13 y^{\prime }+36 y = x \,{\mathrm e}^{4 x} \]

23577

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

23578

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

23581

\[ {} x^{2} y^{\prime \prime }+4 x y^{\prime }-10 y = x \ln \left (x \right ) \]

23582

\[ {} 3 x^{2} y^{\prime \prime }-2 x y^{\prime }-8 y = 5+3 x \]

23583

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

23584

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

23586

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

23587

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

23589

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

23591

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

23592

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

23593

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

23594

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

23595

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

23598

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

23599

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

23600

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

23601

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

23604

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

23606

\[ {} y^{\prime \prime }+4 y = 4 x^{3}-8 x^{2}-14 x +7 \]

23608

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

23609

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

23610

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

23611

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

23612

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

23613

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

23614

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

23615

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

23616

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

23617

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

23618

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

23619

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

23620

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

23621

\[ {} y^{\prime \prime }-7 y^{\prime }-8 y = {\mathrm e}^{x} \left (x^{2}+2\right ) \]

23622

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

23623

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

23624

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

23625

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

23626

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

23628

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

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

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

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

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