Internal problem ID [10964]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number: Problem 2(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y-{\mathrm e}^{2 t} t^{2}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([diff(y(t),t$2)-4*diff(y(t),t)+4*y(t)=t^2*exp(2*t),y(0) = 1, D(y)(0) = 2],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{2 t} \left (1+\frac {t^{4}}{12}\right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 19
DSolve[{y''[t]-4*y'[t]+4*y[t]==t^2*Exp[2*t],{y[0]==1,y'[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{12} e^{2 t} \left (t^4+12\right ) \\ \end{align*}