Internal problem ID [12233]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+\frac {y}{x}={\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve([diff(y(x),x)+1/x*y(x)=exp(x),y(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {1+{\mathrm e}^{x} \left (x -1\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 18
DSolve[{y'[x]+1/x*y[x]==Exp[x],{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x (x-1)+1}{x} \]