Internal problem ID [461]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.1. Page 40
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {2 y+y^{\prime }-{\mathrm e}^{-2 t} t=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 15
dsolve([2*y(t)+diff(y(t),t) = t/exp(2*t),y(1) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (t^{2}-1\right ) {\mathrm e}^{-2 t}}{2} \]
✓ Solution by Mathematica
Time used: 0.063 (sec). Leaf size: 19
DSolve[{2*y[t]+y'[t] == t/Exp[2*t],y[1]==0},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} e^{-2 t} \left (t^2-1\right ) \\ \end{align*}