4.3.12 Problems 1101 to 1200

Table 4.307: Second order ode

#

ODE

Mathematica

Maple

Sympy

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

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

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

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

5916

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

5917

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

5918

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

5919

\[ {} 6 y^{\prime \prime }-11 y^{\prime }+4 y = 0 \]

5920

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

5925

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

5926

\[ {} y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y = 0 \]

5928

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

5931

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

5937

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]

5938

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

5940

\[ {} y^{\prime \prime }-4 y^{\prime }+20 y = 0 \]

5945

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

5946

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

5947

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]

5948

\[ {} y^{\prime \prime }-4 y^{\prime }+20 y = 0 \]

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

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

5995

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

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

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

6000

\[ {} \left (y+1\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2} \]

6001

\[ {} r^{\prime \prime } = -\frac {k}{r^{2}} \]

6002

\[ {} y^{\prime \prime } = \frac {3 k y^{2}}{2} \]

6003

\[ {} y^{\prime \prime } = 2 k y^{3} \]

6004

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

6005

\[ {} r^{\prime \prime } = \frac {h^{2}}{r^{3}}-\frac {k}{r^{2}} \]

6006

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

6007

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

6008

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

6009

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

6010

\[ {} \left (y+1\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2} \]

6011

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

6012

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

6013

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

6014

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

6015

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