4.27.24 Problems 2301 to 2400

Table 4.1599: Second order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

Sympy

23616

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

23617

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

23620

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

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

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

23626

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

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

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

23650

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

23651

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

23652

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

23653

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

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

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

23665

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

23670

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

23747

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

23750

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

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

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

23874

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

23879

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

23880

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

23964

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

24044

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

24045

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

24097

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

24098

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

24099

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

24100

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

24101

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

24102

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

24103

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

24104

\[ {} y^{\prime \prime }-2 y^{\prime }+y = 1+2 x +3 \,{\mathrm e}^{x} \]

24105

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

24109

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

24111

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

24120

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

24121

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

24122

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

24123

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

24129

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

24132

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

24135

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

24137

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

24138

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

24141

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

24145

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

24146

\[ {} y^{\prime \prime }+3 y = -x^{6}+x^{4} \]

24147

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = x^{2} \]

24149

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

24161

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

24162

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

24169

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

24170

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

24171

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

24174

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

24176

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