4.5.17 Problems 1601 to 1700

Table 4.681: Second ODE non-homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

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

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

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

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

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

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

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

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

14929

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

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

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

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

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

15071

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

15072

\[ {} x^{\prime \prime }-x = \frac {1}{t} \]

15073

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

15074

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

15075

\[ {} x^{\prime \prime }-4 x^{\prime } = \tan \left (t \right ) \]

15076

\[ {} \left (\tan \left (x \right )^{2}-1\right ) y^{\prime \prime }-4 \tan \left (x \right )^{3} y^{\prime }+2 y \sec \left (x \right )^{4} = \left (\tan \left (x \right )^{2}-1\right ) \left (1-2 \sin \left (x \right )^{2}\right ) \]

15181

\[ {} y^{\prime \prime }-6 y^{\prime }+10 y = 100 \]

15182

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

15184

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

15185

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

15186

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

15188

\[ {} x^{\prime \prime }-4 x^{\prime }+4 x = {\mathrm e}^{t}+{\mathrm e}^{2 t}+1 \]

15189

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

15190

\[ {} x^{3} x^{\prime \prime }+1 = 0 \]

15197

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

15199

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

15203

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

15204

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

15206

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

15207

\[ {} \left (x^{2}-1\right ) y^{\prime \prime }-6 y = 1 \]

15212

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

15215

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

15216

\[ {} x^{\prime \prime }+10 x^{\prime }+25 x = 2^{t}+t \,{\mathrm e}^{-5 t} \]

15222

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

15241

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

15251

\[ {} 2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y = 1 \]

15253

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

15254

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

15259

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