69.1.136 problem 195

Internal problem ID [14289]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 195
Date solved : Tuesday, January 28, 2025 at 06:25:49 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{x}&={\mathrm e}^{x} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 16

dsolve([diff(y(x),x)+1/x*y(x)=exp(x),y(1) = 1],y(x), singsol=all)
 

\[ y = \frac {\left (x -1\right ) {\mathrm e}^{x}+1}{x} \]

✓ Solution by Mathematica

Time used: 0.067 (sec). Leaf size: 18

DSolve[{D[y[x],x]+1/x*y[x]==Exp[x],{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x (x-1)+1}{x} \]