Internal problem ID [467]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.1. Page 40
Problem number: 20.
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 }-t=0} \end {gather*} With initial conditions \begin {align*} [y \left (\ln \relax (2)\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([(1+t)*y(t)+t*diff(y(t),t) = t,y(ln(2)) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {t -1+2 \,{\mathrm e}^{-t}}{t} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 19
DSolve[{(1+t)*y[t]+t*y'[t]== t,y[Log[2]]==1},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {t+2 e^{-t}-1}{t} \\ \end{align*}