Internal problem ID [10961]
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(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+3 y-9 t=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+3*y(t)=9*t,y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = 3 t +2 \,{\mathrm e}^{-t} \cos \left (\sqrt {2}\, t \right )-2 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 13
DSolve[{y''[t]+2*y''[t]+3*y[t]==9*t,{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 3 t-2 \sin (t) \\ \end{align*}