4.20.18 Problems 1701 to 1800

Table 4.1233: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

8644

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

8646

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 50 t -100 \]

8647

\[ {} y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -3} \]

8648

\[ {} 9 y^{\prime \prime }-6 y^{\prime }+y = 0 \]

8649

\[ {} y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-3 t}-{\mathrm e}^{-5 t} \]

8650

\[ {} y^{\prime \prime }+10 y^{\prime }+24 y = 144 t^{2} \]

8651

\[ {} y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right . \]

8652

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right . \]

8653

\[ {} y^{\prime \prime }+y^{\prime }-2 y = \left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right . \]

8654

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right . \]

8655

\[ {} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <1 \\ 0 & 1<t \end {array}\right . \]

8656

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \]

8657

\[ {} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right . \]

8658

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

8659

\[ {} y^{\prime \prime }+16 y = 4 \delta \left (t -3 \pi \right ) \]

8660

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

8661

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right ) \]

8662

\[ {} 4 y^{\prime \prime }+24 y^{\prime }+37 y = 17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right ) \]

8663

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 10 \sin \left (t \right )+10 \delta \left (t -1\right ) \]

8664

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right ) \]

8665

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

8666

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )+\delta \left (t -2\right ) \]

8667

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (t -\pi \right ) \]

8764

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

8803

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

8804

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

8805

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

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

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

8815

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

8816

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 \sin \left (t \right )-5 \cos \left (t \right ) \]

8817

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

8820

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

8822

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

8823

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

8824

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

8825

\[ {} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \sin \left (3 x \right ) \]

8826

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

8827

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

8840

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

8867

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

8868

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

8871

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

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

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

8926

\[ {} y^{\prime \prime \prime }-8 y = 0 \]

8927

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

8928

\[ {} y^{\prime \prime \prime }-5 y^{\prime \prime }+6 y^{\prime } = 0 \]

8929

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

8930

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

8931

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

8932

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

8933

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

8934

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

8935

\[ {} y^{\left (5\right )}-y^{\prime \prime \prime \prime }-y^{\prime }+y = 0 \]

8936

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

8937

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

8938

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

8939

\[ {} y^{\left (5\right )}+2 y = 0 \]

8940

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

8941

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

8942

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

8943

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

8944

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

8945

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

8946

\[ {} y^{\prime \prime \prime }-8 y = {\mathrm e}^{i x} \]

8947

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

8948

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

8949

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

8950

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