29.18.30 problem 508

Internal problem ID [5104]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 508
Date solved : Tuesday, March 04, 2025 at 07:57:11 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} x y y^{\prime }+x^{4}-y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 30

ode:=x*y(x)*diff(y(x),x)+x^4-y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.471 (sec). Leaf size: 43

ode=x y[x] D[y[x],x]+x^4-y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\sqrt {-x^4+c_1 x^2} \\ y(x)\to \sqrt {-x^4+c_1 x^2} \\ \end{align*}

✓ Sympy. Time used: 0.382 (sec). Leaf size: 26

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

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