23.2.183 problem 188

Internal problem ID [5538]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 188
Date solved : Tuesday, September 30, 2025 at 12:51:43 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} x^{4} {y^{\prime }}^{2}+x y^{2} y^{\prime }-y^{3}&=0 \end{align*}

✓ Maple. Time used: 0.168 (sec). Leaf size: 129

ode:=x^4*diff(y(x),x)^2+x*y(x)^2*diff(y(x),x)-y(x)^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -4 x^{2} \\ y &= 0 \\ y &= \frac {\left (\sqrt {2}\, c_1 -2 x \right ) x \,c_1^{2}}{2 c_1^{2}-4 x^{2}} \\ y &= -\frac {\left (\sqrt {2}\, c_1 +2 x \right ) x \,c_1^{2}}{2 c_1^{2}-4 x^{2}} \\ y &= -\frac {2 \left (-c_1 x +\sqrt {2}\right ) x}{c_1 \left (c_1^{2} x^{2}-2\right )} \\ y &= \frac {2 \left (c_1 x +\sqrt {2}\right ) x}{c_1 \left (c_1^{2} x^{2}-2\right )} \\ \end{align*}

✓ Mathematica. Time used: 0.402 (sec). Leaf size: 79

ode=x^4 (D[y[x],x])^2+x y[x]^2 D[y[x],x]-y[x]^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x (\cosh (2 c_1)+\sinh (2 c_1))}{x+i \cosh (c_1)+i \sinh (c_1)}\\ y(x)&\to \frac {x (\cosh (2 c_1)+\sinh (2 c_1))}{-x+i \cosh (c_1)+i \sinh (c_1)}\\ y(x)&\to 0 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), x)**2 + x*y(x)**2*Derivative(y(x), x) - y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (sqrt((4*x**2 + y(x))*y(x)**3) - y(x)**2)/