69.1.66 problem 94

Internal problem ID [14140]
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 : Wednesday, March 05, 2025 at 10:36:35 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 14

ode:=y(x) = y(x)*diff(y(x),x)+diff(y(x),x)-diff(y(x),x)^2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= x +c_{1} \\ y &= {\mathrm e}^{x} c_{1} \\ \end{align*}

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

ode=y[x]==y[x]*D[y[x],x]+D[y[x],x]-(D[y[x],x])^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.135 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)*Derivative(y(x), x) + y(x) + Derivative(y(x), x)**2 - Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} + x, \ y{\left (x \right )} = C_{1} e^{x}\right ] \]