Internal problem ID [10971]
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(j)[k].
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 y^{\prime \prime }-4 y^{\prime }+y-t^{2}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -12, y^{\prime }\left (0\right ) = 7] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve([4*diff(y(t),t$2)-4*diff(y(t),t)+y(t)=t^2,y(0) = -12, D(y)(0) = 7],y(t), singsol=all)
\[ y \left (t \right ) = \left (17 t -36\right ) {\mathrm e}^{\frac {t}{2}}+t^{2}+8 t +24 \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 25
DSolve[{4*y''[t]-4*y'[t]+y[t]==t^2,{y[0]==-12,y'[0]==7}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t (t+8)+e^{t/2} (17 t-36)+24 \\ \end{align*}