4.5.7 Problems 601 to 700

Table 4.503: Second ODE non-homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

4488

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

4497

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

4498

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

4499

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

4500

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

4501

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

4502

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

4503

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

4504

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

4505

\[ {} y^{\prime \prime }+2 y^{\prime }+y = 15 \,{\mathrm e}^{-x} \sqrt {1+x} \]

4506

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

4507

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

4508

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

4509

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

4510

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

4512

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

4514

\[ {} y^{\prime \prime }+4 y^{\prime }+3 y = 60 \cos \left (3 t \right ) \]

4515

\[ {} y^{\prime \prime }+y^{\prime }-2 y = 9 \,{\mathrm e}^{-2 t} \]

4516

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

4517

\[ {} y^{\prime \prime }+4 y = 8 \sin \left (2 t \right ) \]

4518

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

4519

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

4520

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 8 \,{\mathrm e}^{t} \sin \left (2 t \right ) \]

4521

\[ {} y^{\prime \prime }+y^{\prime }-2 y = 54 t \,{\mathrm e}^{-2 t} \]

4522

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right ) \]

4523

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

4524

\[ {} y^{\prime \prime }+4 y = 8 \sin \left (2 t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \]

4525

\[ {} y^{\prime \prime }+4 y = 8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (t -2\right ) \]

4526

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

4527

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = \delta \left (t -2\right ) \]

4528

\[ {} y^{\prime \prime }+4 y = 4 \operatorname {Heaviside}\left (t -\pi \right )+2 \delta \left (t -\pi \right ) \]

5950

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

5951

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \]

5952

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

5953

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

5954

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

5955

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right ) \]

5956

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

5957

\[ {} y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \]

5958

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

5959

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

5960

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

5961

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

5962

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

5963

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

5964

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

5965

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

5966

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

5967

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

5968

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

5969

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

5970

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

5971

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

5972

\[ {} y^{\prime \prime }+9 y = 8 \cos \left (x \right ) \]

5973

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

5974

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

5975

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

5976

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

5977

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

5978

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

5979

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

5980

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \]

5981

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

5982

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

5983

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

5984

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

5985

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

5986

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

5987

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

5988

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

5989

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

5990

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

5991

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

5992

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

5993

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

5994

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

5996

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

5997

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

5998

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

5999

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

6008

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

6014

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

6015

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

6151

\[ {} y^{\prime \prime }-4 y^{\prime } = 10 \]

6152

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = 16 \]

6153

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

6154

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 24 \,{\mathrm e}^{-3 x} \]

6155

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

6156

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 12 \,{\mathrm e}^{-x} \]

6157

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

6158

\[ {} y^{\prime \prime }-16 y = 40 \,{\mathrm e}^{4 x} \]

6159

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

6160

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

6161

\[ {} y^{\prime \prime }+2 y^{\prime }+10 y = 100 \cos \left (4 x \right ) \]

6162

\[ {} y^{\prime \prime }+4 y^{\prime }+12 y = 80 \sin \left (2 x \right ) \]

6163

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

6164

\[ {} y^{\prime \prime }+8 y^{\prime }+25 y = 120 \sin \left (5 x \right ) \]

6165

\[ {} 5 y^{\prime \prime }+12 y^{\prime }+20 y = 120 \sin \left (2 x \right ) \]

6166

\[ {} y^{\prime \prime }+9 y = 30 \sin \left (3 x \right ) \]

6167

\[ {} y^{\prime \prime }+16 y = 16 \cos \left (4 x \right ) \]