4.27.20 Problems 1901 to 2000

Table 4.1591: Second order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

Sympy

20172

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

20175

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

20176

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

20177

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

20178

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

20182

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

20183

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

20184

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

20190

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

20191

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

20192

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

20196

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

20198

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

20202

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

20203

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

20205

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

20241

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

20278

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

20281

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

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

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

20469

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

20470

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

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

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

20481

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

20482

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

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

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

20491

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

20494

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

20651

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

20652

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

20655

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

20667

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

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

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

20817

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

20819

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

20822

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

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

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

20887

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

20888

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

20918

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

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

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

20993

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

20994

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

20995

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

21031

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

21032

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

21033

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

21034

\[ {} y^{\prime \prime }+4 y = \delta \left (t -1\right ) \]

21035

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -1\right ) \]

21036

\[ {} y^{\prime \prime }+6 y^{\prime }+18 y = 2 \operatorname {Heaviside}\left (\pi -t \right ) \]

21114

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

21115

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

21116

\[ {} u^{\prime \prime }+2 a u^{\prime }+\omega ^{2} u = c \cos \left (\omega t \right ) \]

21246

\[ {} x^{\prime \prime }-4 x = t \]

21247

\[ {} x^{\prime \prime }-4 x = 4 t^{2} \]

21248

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

21249

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

21250

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

21251

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

21252

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

21253

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

21254

\[ {} x^{\prime \prime }-4 x^{\prime }+13 x = 20 \,{\mathrm e}^{t} \]

21255

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

21256

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

21257

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