83.18.10 problem 10

Internal problem ID [19141]
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, March 13, 2025 at 01:45:10 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (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 \left (x \right ) &= \frac {c_{1}}{x} \\ y \left (x \right ) &= x +c_{1} \\ \end{align*}

✓ Mathematica. Time used: 0.035 (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: 0.137 (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)
 

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