Internal problem ID [10965]
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(e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+9 y-{\mathrm e}^{-2 t}=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = -{\frac {2}{13}}, y^{\prime }\left (0\right ) = {\frac {1}{13}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve([diff(y(t),t$2)+9*y(t)=exp(-2*t),y(0) = -2/13, D(y)(0) = 1/13],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\sin \left (3 t \right )}{13}-\frac {3 \cos \left (3 t \right )}{13}+\frac {{\mathrm e}^{-2 t}}{13} \]
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 25
DSolve[{y''[t]+9*y[t]==Exp[-2*t],{y[0]==-2/13,y'[0]==1/13}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{13} \left (e^{-2 t}+\sin (3 t)-3 \cos (3 t)\right ) \\ \end{align*}