Internal problem ID [457]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.1. Page 40
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {t y^{\prime }-y-t^{2} {\mathrm e}^{-t}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(-y(t)+t*diff(y(t),t) = t^2/exp(t),y(t), singsol=all)
\[ y \left (t \right ) = \left (-{\mathrm e}^{-t}+c_{1} \right ) t \]
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 16
DSolve[-y[t]+t*y'[t] == t^2/Exp[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t (\sinh (t)-\cosh (t)+c_1) \\ \end{align*}