89.28.6 problem 6

Internal problem ID [24894]
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. Exercises at page 229
Problem number : 6
Date solved : Thursday, October 02, 2025 at 10:49:10 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\begin{align*} y &= \ln \left (x \right )+c_1 \\ y &= c_1 \,{\mathrm e}^{x} \\ \end{align*}

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.139 (sec). Leaf size: 14

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

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