69.1.66 problem 94

Internal problem ID [14219]
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
Date solved : Tuesday, January 28, 2025 at 06:22:25 AM
CAS classification : [_quadrature]

\begin{align*} y&=y^{\prime } y+y^{\prime }-{y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (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 &= x +c_{1} \\ y &= {\mathrm e}^{x} c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 19

DSolve[y[x]==y[x]*D[y[x],x]+D[y[x],x]-(D[y[x],x])^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^x \\ y(x)\to x+c_1 \\ \end{align*}