Internal problem ID [1758]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.4, The method of variation of parameters. Page 154
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {3 y^{\prime \prime }+4 y^{\prime }+y-{\mathrm e}^{-t} \sin \left (t \right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 27
dsolve([3*diff(y(t),t$2)+4*diff(y(t),t)+y(t)=sin(t)*exp(-t),y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {24 \,{\mathrm e}^{-\frac {t}{3}}}{13}+\frac {\left (2 \cos \left (t \right )-3 \sin \left (t \right )-13\right ) {\mathrm e}^{-t}}{13} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 33
DSolve[{3*y''[t]+4*y'[t]+y[t]==Sin[t]*Exp[-t],{y[0]==1,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{13} e^{-t} \left (24 e^{2 t/3}-3 \sin (t)+2 \cos (t)-13\right ) \\ \end{align*}