Internal problem ID [471]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.1. Page 40
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (t +1\right ) y+t y^{\prime }-2 t \,{\mathrm e}^{-t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = a] \end {align*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 21
dsolve([(1+t)*y(t)+t*diff(y(t),t) = 2*t/exp(t),y(1) = a],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (t^{2}+a \,{\mathrm e}-1\right ) {\mathrm e}^{-t}}{t} \]
✓ Solution by Mathematica
Time used: 0.076 (sec). Leaf size: 22
DSolve[{(1+t)*y[t]+t*y'[t] == 2*t/Exp[t],y[1]==a},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {e^{-t} \left (e a+t^2-1\right )}{t} \\ \end{align*}