4.3.26 Problems 2501 to 2600

Table 4.415: Second order ode

#

ODE

Mathematica

Maple

Sympy

8806

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

8807

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

8808

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

8809

\[ {} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0 \]

8810

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

8811

\[ {} \sin \left (x \right ) u^{\prime \prime }+2 \cos \left (x \right ) u^{\prime }+\sin \left (x \right ) u = 0 \]

8813

\[ {} y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1} = 0 \]

8814

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

8819

\[ {} x x^{\prime \prime }-{x^{\prime }}^{2} = 0 \]

8821

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

8822

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

8823

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

8824

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

8826

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

8827

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

8828

\[ {} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0 \]

8831

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

8832

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

8837

\[ {} u^{\prime \prime }-\cot \left (\theta \right ) u^{\prime } = 0 \]

8843

\[ {} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0 \]

8844

\[ {} \left (-x^{2}+1\right ) z^{\prime \prime }+\left (1-3 x \right ) z^{\prime }+k z = 0 \]

8845

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

8851

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

8867

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

8871

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

8872

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

8873

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

8875

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

8898

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

8899

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

8900

\[ {} y^{\prime \prime }+16 y = 0 \]

8901

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

8902

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

8903

\[ {} y^{\prime \prime }-4 y^{\prime }+5 y = 0 \]

8904

\[ {} y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0 \]

8905

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

8906

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

8907

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

8908

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

8909

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

8910

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

8911

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

8912

\[ {} y^{\prime \prime }+\left (1+4 i\right ) y^{\prime }+y = 0 \]

8913

\[ {} y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0 \]

8914

\[ {} y^{\prime \prime }+10 y = 0 \]

8915

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

8916

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

8917

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

8918

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

8919

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

8920

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

8921

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

8922

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

8923

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

8924

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

8925

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

8936

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

8937

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

8943

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

8950

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

8951

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

8952

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

8953

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

8954

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

8955

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

8956

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

8957

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

8960

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

8961

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

8962

\[ {} \left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y = 0 \]

8963

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 0 \]

8964

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

8965

\[ {} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \]

8966

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

8967

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

8968

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

8970

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

8971

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

8972

\[ {} x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

8983

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

8984

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

8985

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0 \]

8986

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

8987

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

8988

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

8990

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

8991

\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+5 y = 0 \]

8992

\[ {} x^{2} y^{\prime \prime }+\left (-2-i\right ) x y^{\prime }+3 i y = 0 \]

8993

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

9045

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

9046

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

9047

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

9048

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

9049

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

9050

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

9051

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

9052

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

9053

\[ {} y^{\prime \prime }+\sin \left (y\right ) = 0 \]

9054

\[ {} y^{\prime \prime }+\sin \left (y\right ) = 0 \]

9063

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