Internal problem ID [1759]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.4, The method of variation of parameters. Page 154
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+4 y-t^{\frac {5}{2}} {\mathrm e}^{-2 t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.025 (sec). Leaf size: 13
dsolve([diff(y(t),t$2)+4*diff(y(t),t)+4*y(t)=t^(5/2)*exp(-2*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {4 t^{\frac {9}{2}} {\mathrm e}^{-2 t}}{63} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 19
DSolve[{y''[t]+4*y'[t]+4*y[t]==t^(5/2)*Exp[-2*t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {4}{63} e^{-2 t} t^{9/2} \\ \end{align*}