56.17.6 problem Ex 6

Internal problem ID [14187]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IV, differential equations of the first order and higher degree than the first. Article 28. Summary. Page 59
Problem number : Ex 6
Date solved : Thursday, October 02, 2025 at 09:25:17 AM
CAS classification : [_rational]

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.279 (sec). Leaf size: 75

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

\begin{align*} y(x)&\to \sqrt {c_1 \left (x^2-\frac {a^2}{1+c_1}\right )}\\ y(x)&\to -i (a-x)\\ y(x)&\to i (a-x)\\ y(x)&\to -i (a+x)\\ y(x)&\to i (a+x) \end{align*}

✗ Sympy

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

Timed Out