29.33.1 problem 963

Internal problem ID [5540]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 33
Problem number : 963
Date solved : Tuesday, March 04, 2025 at 09:51:40 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

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

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

✓ Mathematica. Time used: 0.061 (sec). Leaf size: 65

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

\begin{align*} y(x)\to c_1 x \\ y(x)\to -\sqrt {-x^2+2 c_1} \\ y(x)\to \sqrt {-x^2+2 c_1} \\ y(x)\to -i x \\ y(x)\to i x \\ \end{align*}

✓ Sympy. Time used: 0.549 (sec). Leaf size: 27

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

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} - x^{2}}, \ y{\left (x \right )} = \sqrt {C_{1} - x^{2}}, \ y{\left (x \right )} = C_{1} x\right ] \]