4.20.24 Problems 2301 to 2400

Table 4.1245: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

14755

\[ {} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+7 y^{\prime \prime }-5 y^{\prime }+6 y = 5 \sin \left (x \right )-12 \sin \left (2 x \right ) \]

14756

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

14757

\[ {} y^{\prime \prime }+5 y^{\prime }+4 y = 16 x +20 \,{\mathrm e}^{x} \]

14758

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

14759

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

14760

\[ {} 16 y+8 y^{\prime }+y^{\prime \prime } = 8 \,{\mathrm e}^{-2 x} \]

14761

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 27 \,{\mathrm e}^{-6 x} \]

14762

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = 18 \,{\mathrm e}^{-2 x} \]

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

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

14768

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

14769

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

14770

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y = 3 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-\sin \left (x \right ) \]

14771

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }-4 y = 8 x^{2}+3-6 \,{\mathrm e}^{2 x} \]

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

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

14777

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

14778

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = x \,{\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \]

14779

\[ {} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime }+y = x^{2} {\mathrm e}^{-x}+3 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \]

14780

\[ {} y^{\prime \prime \prime \prime }-16 y = x^{2} \sin \left (2 x \right )+x^{4} {\mathrm e}^{2 x} \]

14781

\[ {} y^{\left (6\right )}+2 y^{\left (5\right )}+5 y^{\prime \prime \prime \prime } = x^{3}+x^{2} {\mathrm e}^{-x}+\sin \left (2 x \right ) {\mathrm e}^{-x} \]

14782

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

14783

\[ {} y^{\prime \prime \prime \prime }+16 y = x \,{\mathrm e}^{\sqrt {2}\, x} \sin \left (\sqrt {2}\, x \right )+{\mathrm e}^{-\sqrt {2}\, x} \cos \left (\sqrt {2}\, x \right ) \]

14784

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

14785

\[ {} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = \sin \left (2 x \right ) \sin \left (x \right ) \]

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

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

14811

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

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

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

14935

\[ {} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y = 20 \sin \left (t \right ) \]

14936

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 36 t \,{\mathrm e}^{4 t} \]

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

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

14959

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

14960

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

14961

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

14962

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

15031

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

15032

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

15033

\[ {} z^{\prime \prime }-4 z^{\prime }+13 z = 0 \]

15034

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

15035

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

15036

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

15037

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

15038

\[ {} 2 z^{\prime \prime }+7 z^{\prime }-4 z = 0 \]

15039

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

15040

\[ {} x^{\prime \prime }+6 x^{\prime }+10 x = 0 \]

15041

\[ {} 4 x^{\prime \prime }-20 x^{\prime }+21 x = 0 \]

15042

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

15043

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

15044

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

15045

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

15046

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

15047

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

15048

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

15049

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

15050

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

15051

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

15052

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

15053

\[ {} x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \]

15054

\[ {} x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \cos \left (3 t \right ) \]

15055

\[ {} x^{\prime \prime }+6 x^{\prime }+10 x = {\mathrm e}^{-2 t} \cos \left (t \right ) \]

15056

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

15057

\[ {} x^{\prime \prime }+x^{\prime }-2 x = 12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t} \]

15058

\[ {} x^{\prime \prime }+4 x = 289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \]

15059

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

15060

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