10.1.24 problem 24

Internal problem ID [1121]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 24
Date solved : Monday, January 27, 2025 at 04:34:08 AM
CAS classification : [_linear]

\begin{align*} \left (1+t \right ) y+t y^{\prime }&=2 t \,{\mathrm e}^{-t} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=a \end{align*}

✓ Solution by Maple

Time used: 0.339 (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)
 

\[ y = \frac {\left (t^{2}+a \,{\mathrm e}-1\right ) {\mathrm e}^{-t}}{t} \]

✓ Solution by Mathematica

Time used: 0.076 (sec). Leaf size: 22

DSolve[{(1+t)*y[t]+t*D[y[t],t] == 2*t/Exp[t],y[1]==a},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {e^{-t} \left (e a+t^2-1\right )}{t} \]