47.1.7 problem 7

Internal problem ID [9727]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 94. Factoring the left member. EXERCISES Page 309
Problem number : 7
Date solved : Tuesday, September 30, 2025 at 06:32:23 PM
CAS classification : [_quadrature]

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

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

ode:=x*diff(y(x),x)^2-(1+x*y(x))*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: 0.007 (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: 0.141 (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)
 

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