Internal problem ID [1755]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.4, The method of variation of parameters. Page 154
Problem number: 2.
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-{\mathrm e}^{2 t} t=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 27
dsolve(diff(y(t),t$2)-4*diff(y(t),t)+4*y(t)=t*exp(2*t),y(t), singsol=all)
\[ y \relax (t ) = c_{2} {\mathrm e}^{2 t}+{\mathrm e}^{2 t} t c_{1}+\frac {{\mathrm e}^{2 t} t^{3}}{6} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 27
DSolve[y''[t]-4*y'[t]+4*y[t]==t*Exp[2*t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{6} e^{2 t} \left (t^3+6 c_2 t+6 c_1\right ) \\ \end{align*}