10.1.20 problem 20

Internal problem ID [1117]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 20
Date solved : Monday, January 27, 2025 at 04:34:00 AM
CAS classification : [_linear]

\begin{align*} \left (1+t \right ) y+t y^{\prime }&=t \end{align*}

With initial conditions

\begin{align*} y \left (\ln \left (2\right )\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

dsolve([(1+t)*y(t)+t*diff(y(t),t) = t,y(ln(2)) = 1],y(t), singsol=all)
 

\[ y = \frac {t -1+2 \,{\mathrm e}^{-t}}{t} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 23

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

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