5.20.19 Problems 1801 to 1900

Table 5.943: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

9082

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

9083

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

9086

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

9089

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

9092

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

9095

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

9096

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

9097

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

9098

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

9099

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

9100

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

9101

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

9102

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

9103

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

9104

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

9105

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

9106

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

9107

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

9108

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

9109

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

9110

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

9111

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

9112

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

9113

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

9114

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

9115

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

9165

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

9564

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

9677

\[ {}y^{\prime \prime }+3 y^{\prime }+4 y = 0 \]

9959

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

9991

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

11011

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

11012

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

11013

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

11014

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

11015

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

11016

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

11017

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

11018

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

11019

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

11044

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

11045

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

11073

\[ {}y^{\prime \prime }+a y^{\prime }+\tan \left (x \right )+b y = 0 \]

11452

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

11455

\[ {}y^{\prime \prime \prime }+3 y^{\prime }-4 y = 0 \]

11456

\[ {}y^{\prime \prime \prime }-a^{2} y^{\prime }-{\mathrm e}^{2 a x} \sin \left (x \right )^{2} = 0 \]

11467

\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime }+10 y = 0 \]

11468

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

11469

\[ {}y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-y a^{3}-{\mathrm e}^{a x} = 0 \]

11470

\[ {}y^{\prime \prime \prime }+\operatorname {a2} y^{\prime \prime }+\operatorname {a1} y^{\prime }+\operatorname {a0} y = 0 \]

11478

\[ {}4 y^{\prime \prime \prime }-8 y^{\prime \prime }-11 y^{\prime }-3 y+18 \,{\mathrm e}^{x} = 0 \]

11535

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

11536

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

11537

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

11538

\[ {}y^{\prime \prime \prime \prime }-12 y^{\prime \prime }+12 y-16 x^{4} {\mathrm e}^{x^{2}} = 0 \]

11539

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

11540

\[ {}y^{\prime \prime \prime \prime }+\left (\lambda +1\right ) a^{2} y^{\prime \prime }+\lambda \,a^{4} y = 0 \]

11545

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y-32 \sin \left (2 x \right )+24 \cos \left (2 x \right ) = 0 \]

11547

\[ {}4 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+11 y^{\prime \prime }-3 y^{\prime }-4 \cos \left (x \right ) = 0 \]

11575

\[ {}f \left (y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y\right )+2 \operatorname {df} \left (y^{\prime \prime \prime }-a^{2} y^{\prime }\right ) = 0 \]

11576

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

11578

\[ {}y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime }-a x -b \sin \left (x \right )-c \cos \left (x \right ) = 0 \]

11579

\[ {}y^{\left (6\right )}+y-\sin \left (\frac {3 x}{2}\right ) \sin \left (\frac {x}{2}\right ) = 0 \]

11582

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

11584

\[ {}x \left (a y^{\prime }+b y^{\prime \prime }+c y^{\prime \prime \prime }+e y^{\prime \prime \prime \prime }\right ) y = 0 \]

11845

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

12501

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

12511

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

12919

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

12920

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]

12921

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

12922

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

12923

\[ {}4 y^{\prime \prime \prime }-3 y^{\prime }+y = 0 \]

12924

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

12925

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

12926

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

12927

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

12928

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

12929

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

12930

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

12931

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

12932

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

12933

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

12934

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

12935

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

12936

\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = x \]

12937

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

12938

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

12939

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

12940

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

12941

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

12942

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

12943

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

12944

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

12945

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

12946

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

12947

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

12952

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

12953

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

12954

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