89.32.22 problem 25

Internal problem ID [24982]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 16. Equations of order one and higher degree. Miscellaneous Exercises at page 246
Problem number : 25
Date solved : Thursday, October 02, 2025 at 11:45:19 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2} x +y \left (1-x \right ) y^{\prime }-y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=x*diff(y(x),x)^2+y(x)*(1-x)*diff(y(x),x)-y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {c_1}{x} \\ y &= c_1 \,{\mathrm e}^{x} \\ \end{align*}

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 26

ode=x*D[y[x],x]^2+y[x]*(1-x)*D[y[x],x]-y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^x\\ y(x)&\to \frac {c_1}{x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.090 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x)**2 + (1 - x)*y(x)*Derivative(y(x), x) - y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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