Internal problem ID [12483]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 94.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y-y y^{\prime }-y^{\prime }+{y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(y(x)=y(x)*diff(y(x),x)+diff(y(x),x)-diff(y(x),x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= c_{1} +x \\ y \left (x \right ) &= c_{1} {\mathrm e}^{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 19
DSolve[y[x]==y[x]*y'[x]+y'[x]-(y'[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x \\ y(x)\to x+c_1 \\ \end{align*}