23.1.521 problem 511

Internal problem ID [5128]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 511
Date solved : Tuesday, September 30, 2025 at 11:43:34 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (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 &= \sqrt {-x^{2}+c_1}\, x \\ y &= -\sqrt {-x^{2}+c_1}\, x \\ \end{align*}

✓ Mathematica. Time used: 0.315 (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: 0.225 (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)
 

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