4.20.35 Problems 3401 to 3500

Table 4.971: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

17619

\[ {} y^{\prime \prime }+4 y = g \left (t \right ) \]

17630

\[ {} y^{\prime \prime }+y = g \left (t \right ) \]

17633

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

17634

\[ {} 9 y^{\prime \prime }+12 y^{\prime }+4 y = 0 \]

17635

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

17636

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

17637

\[ {} y^{\prime \prime }-2 y^{\prime }+2 y = t^{2} {\mathrm e}^{t}+7 \]

17638

\[ {} y^{\prime \prime }-5 y^{\prime }-6 y = t^{2}+7 \]

17639

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

17640

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = t \cos \left (2 t \right ) \]

17641

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

17642

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

17643

\[ {} y^{\prime \prime }+16 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

17644

\[ {} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \]

17645

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

17646

\[ {} y^{\prime \prime }-4 y^{\prime }-12 y = 0 \]

17647

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

17648

\[ {} y^{\prime \prime }-8 y^{\prime }+25 y = 0 \]

17649

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

17650

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

17651

\[ {} y^{\prime \prime }+4 y^{\prime }+29 y = {\mathrm e}^{-2 t} \sin \left (5 t \right ) \]

17652

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

17653

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

17654

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

17655

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

17656

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

17657

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

17658

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

17670

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

17671

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

17672

\[ {} y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \]

17673

\[ {} y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -\pi \right ) \sin \left (t \right ) \]

17674

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & 10\le t \end {array}\right . \]

17675

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

17676

\[ {} y^{\prime \prime }+y = \operatorname {Heaviside}\left (t -3 \pi \right ) \]

17677

\[ {} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \]

17678

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

17679

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

17680

\[ {} y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \]

17681

\[ {} y^{\prime \prime \prime \prime }-y = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right ) \]

17682

\[ {} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 1-\operatorname {Heaviside}\left (t -\pi \right ) \]

17683

\[ {} u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )}{2} \]

17684

\[ {} u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right . \]

17685

\[ {} u^{\prime \prime }+\frac {u^{\prime }}{4}+u = 2 \left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right ) \]

17686

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

17687

\[ {} y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \]

17688

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -\pi \right )+\operatorname {Heaviside}\left (t -10\right ) \]

17689

\[ {} y^{\prime \prime }-y = -20 \delta \left (t -3\right ) \]

17690

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

17691

\[ {} y^{\prime \prime }+4 y = \delta \left (t -4 \pi \right ) \]

17692

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

17693

\[ {} y^{\prime \prime }+4 y = 2 \delta \left (t -\frac {\pi }{4}\right ) \]

17694

\[ {} y^{\prime \prime }+y = \operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )+3 \delta \left (t -\frac {3 \pi }{2}\right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \]

17695

\[ {} 2 y^{\prime \prime }+y^{\prime }+6 y = \delta \left (t -\frac {\pi }{6}\right ) \sin \left (t \right ) \]

17696

\[ {} y^{\prime \prime }+2 y^{\prime }+2 y = \cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right ) \]

17697

\[ {} y^{\prime \prime \prime \prime }-y = \delta \left (t -1\right ) \]

17698

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

17699

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{4}+y = \delta \left (t -1\right ) \]

17700

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

17701

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{5}+y = k \delta \left (t -1\right ) \]

17702

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{10}+y = k \delta \left (t -1\right ) \]

17703

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

17704

\[ {} y^{\prime \prime }+6 y^{\prime }+25 y = \sin \left (\alpha t \right ) \]

17705

\[ {} 4 y^{\prime \prime }+4 y^{\prime }+17 y = g \left (t \right ) \]

17706

\[ {} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 1-\operatorname {Heaviside}\left (t -\pi \right ) \]

17707

\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = g \left (t \right ) \]

17708

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (\alpha t \right ) \]

17709

\[ {} y^{\prime \prime \prime \prime }-16 y = g \left (t \right ) \]

17710

\[ {} y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y = g \left (t \right ) \]

17711

\[ {} \frac {7 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right ) \]

17712

\[ {} \frac {8 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right ) \]

17715

\[ {} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+3 y = t \]

17721

\[ {} y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+4 y = 0 \]

17729

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

17730

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

17731

\[ {} y^{\prime \prime \prime }+4 y^{\prime \prime }-4 y^{\prime }-16 y = 0 \]

17732

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

17814

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

17891

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

17925

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

17926

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

17928

\[ {} y^{\prime \prime }+p_{1} y^{\prime }+p_{2} y = 0 \]

17931

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

17932

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

17933

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

17934

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

17935

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

17936

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

17937

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

17938

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

17939

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

17940

\[ {} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = \left (1+x \right ) {\mathrm e}^{x} \]

17941

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

17942

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

17943

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

17944

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

17945

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

17946

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

17981

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

17982

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