4.3.52 Problems 5101 to 5200

Table 4.467: Second order ode

#

ODE

Mathematica

Maple

Sympy

14763

\[ {} y^{\prime \prime }-10 y^{\prime }+29 y = 8 \,{\mathrm e}^{5 x} \]

14764

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 8 \sin \left (3 x \right ) \]

14765

\[ {} y^{\prime \prime }-y^{\prime }-6 y = 8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \]

14766

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

14767

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

14768

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

14769

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

14772

\[ {} y^{\prime \prime }-6 y^{\prime }+8 y = x^{3}+x +{\mathrm e}^{-2 x} \]

14773

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

14774

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{-2 x} \left (\cos \left (x \right )+1\right ) \]

14775

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = x^{4} {\mathrm e}^{x}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \]

14776

\[ {} y^{\prime \prime }+6 y^{\prime }+13 y = x \,{\mathrm e}^{-3 x} \sin \left (2 x \right )+x^{2} {\mathrm e}^{-2 x} \sin \left (3 x \right ) \]

14786

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

14787

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

14788

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

14789

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

14790

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

14791

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

14792

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{-2 x} \sec \left (x \right ) \]

14793

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

14794

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 x}}{x^{3}} \]

14795

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

14796

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

14797

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

14798

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

14799

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

14800

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

14801

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

14802

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

14803

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

14804

\[ {} x^{2} y^{\prime \prime }-6 x y^{\prime }+10 y = 3 x^{4}+6 x^{3} \]

14805

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

14806

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

14807

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

14808

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

14809

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

14810

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

14812

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

14813

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

14814

\[ {} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 0 \]

14815

\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]

14816

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

14817

\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \]

14818

\[ {} 3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0 \]

14819

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \]

14820

\[ {} 9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

14821

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y = 0 \]

14825

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 4 x -6 \]

14826

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \]

14827

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

14828

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

14829

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

14831

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

14832

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

14833

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

14834

\[ {} x^{2} y^{\prime \prime }-2 y = 4 x -8 \]

14835

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = -6 x^{3}+4 x^{2} \]

14836

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 10 x^{2} \]

14837

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \]

14838

\[ {} x^{2} y^{\prime \prime }-6 y = \ln \left (x \right ) \]

14839

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

14840

\[ {} \left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y = 0 \]

14927

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

14928

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

14929

\[ {} y^{\prime \prime }+4 y = 8 \]

14930

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

14931

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 18 \,{\mathrm e}^{-t} \sin \left (3 t \right ) \]

14932

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

14933

\[ {} y^{\prime \prime }+7 y^{\prime }+10 y = 4 t \,{\mathrm e}^{-3 t} \]

14934

\[ {} y^{\prime \prime }-8 y^{\prime }+15 y = 9 t \,{\mathrm e}^{2 t} \]

14937

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

14938

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = \left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right . \]

14939

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right . \]

14940

\[ {} y^{\prime \prime }+6 y^{\prime }+8 y = \left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \]

14941

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

14942

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

14943

\[ {} t x^{\prime \prime }-2 x^{\prime }+9 t^{5} x = 0 \]

14945

\[ {} \left (t^{3}-2 t^{2}\right ) x^{\prime \prime }-\left (t^{3}+2 t^{2}-6 t \right ) x^{\prime }+\left (3 t^{2}-6\right ) x = 0 \]

14947

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

14948

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

14949

\[ {} t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x = 0 \]

14950

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

14951

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

14952

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

14953

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

14954

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

14955

\[ {} \left (t^{4}+t^{2}\right ) x^{\prime \prime }+2 t^{3} x^{\prime }+3 x = 0 \]

14956

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

14957

\[ {} f \left (t \right ) x^{\prime \prime }+x g \left (t \right ) = 0 \]

14958

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

14959

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

14960

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

14961

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

14962

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

14963

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

14964

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

14965

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

14966

\[ {} -\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y = 0 \]

14979

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

14980

\[ {} x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x = 0 \]