4.5.10 Problems 901 to 1000

Table 4.509: Second ODE non-homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

7498

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

7499

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

7500

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

7501

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

7520

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

7521

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

7522

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

7524

\[ {} p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u = f \left (x \right ) \]

7536

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 50 \,{\mathrm e}^{2 x} \]

7537

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = 50 \,{\mathrm e}^{2 x} \]

7538

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

7540

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

7541

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

7581

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

7589

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

7629

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

7630

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

7631

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

7632

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

7633

\[ {} y^{\prime \prime }-4 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x}+2 x^{2} \]

7634

\[ {} y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \]

7635

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

7636

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

7637

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

7638

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

7639

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

7664

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

7665

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

7666

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

7667

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

7668

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

7669

\[ {} y^{\prime \prime }+9 y = x^{2} {\mathrm e}^{3 x} \]

7670

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

7671

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

7702

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{2} \]

7704

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

7707

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

7759

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

7760

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

7764

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

7765

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

7823

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

7824

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

7909

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

7911

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

7915

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

7916

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

7936

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

7970

\[ {} y^{\prime \prime }+3 y^{\prime }-10 y = 6 \,{\mathrm e}^{4 x} \]

7971

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

7972

\[ {} y^{\prime \prime }+10 y^{\prime }+25 y = 14 \,{\mathrm e}^{-5 x} \]

7973

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 25 x^{2}+12 \]

7974

\[ {} y^{\prime \prime }-y^{\prime }-6 y = 20 \,{\mathrm e}^{-2 x} \]

7975

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \]

7976

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

7977

\[ {} y^{\prime \prime }-2 y^{\prime } = 12 x -10 \]

7978

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

7979

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

7980

\[ {} y^{\prime \prime }+y^{\prime } = 10 x^{4}+2 \]

7981

\[ {} y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \]

7982

\[ {} y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \]

7983

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

7985

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

7986

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

7987

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x} \]

7988

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

7989

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

7990

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

7991

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

7992

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

7993

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

7994

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

7995

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

7996

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

7997

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

7998

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

7999

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

8000

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

8001

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

8002

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

8003

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

8004

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

8043

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

8044

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

8045

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

8046

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

8048

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

8049

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

8050

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

8051

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

8052

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

8053

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

8054

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

8055

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

8056

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

8057

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

8058

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

8059

\[ {} y^{\prime \prime }+9 y = \sec \left (2 x \right ) \]

8060

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

8061

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