4.2.39 Problems 3801 to 3900

Table 4.245: Second order linear ODE

#

ODE

Mathematica

Maple

Sympy

13577

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

13578

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

13579

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

13580

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

13581

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

13582

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

13583

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

13585

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

13587

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

13588

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

13589

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

13590

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

13591

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

13592

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

13593

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

13594

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

13595

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

13596

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

13597

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

13598

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

13599

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

13600

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

13601

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

13602

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

13603

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

13604

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

13605

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

13606

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

13671

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

13672

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

13673

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

13674

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

13675

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

13676

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

13677

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

13678

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

13679

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

13680

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

13681

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

13682

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

13683

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

13684

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

13685

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

13686

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

13687

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

13688

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

13689

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

13690

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

13691

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

13692

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

13693

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

13694

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

13695

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

13696

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

13697

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

13698

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

13699

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

13700

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

13705

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

13706

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

13707

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

13708

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

13709

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

13710

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

13711

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

13712

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

13713

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

13714

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

13715

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

13716

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

13717

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

13718

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

13719

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

13720

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

13721

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

13722

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

13723

\[ {} 4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0 \]

13724

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

13725

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

13726

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

13727

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

13821

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

13822

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

13824

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

13825

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

13826

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

13828

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

13836

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-\frac {1}{25}\right ) y = 0 \]

13839

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

13840

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

13843

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

13844

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

13846

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

13847

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

13852

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

13853

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

13855

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

13856

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

13862

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

13879

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