29.25.9 problem 706

Internal problem ID [5296]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 706
Date solved : Tuesday, March 04, 2025 at 09:16:33 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (x^{2}-y^{4}\right ) y^{\prime }&=x y \end{align*}

✓ Maple. Time used: 0.188 (sec). Leaf size: 97

ode:=(x^2-y(x)^4)*diff(y(x),x) = x*y(x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y \left (x \right ) &= -\frac {\sqrt {-2 \sqrt {c_{1}^{2}-4 x^{2}}+2 c_{1}}}{2} \\ y \left (x \right ) &= \frac {\sqrt {-2 \sqrt {c_{1}^{2}-4 x^{2}}+2 c_{1}}}{2} \\ y \left (x \right ) &= -\frac {\sqrt {2 \sqrt {c_{1}^{2}-4 x^{2}}+2 c_{1}}}{2} \\ y \left (x \right ) &= \frac {\sqrt {2 \sqrt {c_{1}^{2}-4 x^{2}}+2 c_{1}}}{2} \\ \end{align*}

✓ Mathematica. Time used: 2.171 (sec). Leaf size: 122

ode=(x^2-y[x]^4)D[y[x],x]==x y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\sqrt {-\sqrt {-x^2+c_1{}^2}-c_1} \\ y(x)\to \sqrt {-\sqrt {-x^2+c_1{}^2}-c_1} \\ y(x)\to -\sqrt {\sqrt {-x^2+c_1{}^2}-c_1} \\ y(x)\to \sqrt {\sqrt {-x^2+c_1{}^2}-c_1} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 4.475 (sec). Leaf size: 75

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x) + (x**2 - y(x)**4)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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