77.18.10 problem 10

Internal problem ID [20505]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (A) at page 53
Problem number : 10
Date solved : Thursday, October 02, 2025 at 06:03:40 PM
CAS classification : [_quadrature]

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

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

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

\begin{align*} y &= \frac {c_1}{x} \\ y &= x +c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.085 (sec). Leaf size: 10

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

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