Internal problem ID [12165]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 96.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y-x y^{\prime }-y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 9
dsolve(y(x)=x*diff(y(x),x)+diff(y(x),x),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x +1\right ) \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 16
DSolve[y[x]==x*y'[x]+y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x+1) y(x)\to 0 \end{align*}