23.2.154 problem 157

Internal problem ID [5509]
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 : 157
Date solved : Tuesday, September 30, 2025 at 12:46:03 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x^{2} {y^{\prime }}^{2}+x \left (x^{3}-2 y\right ) y^{\prime }-\left (2 x^{3}-y\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.052 (sec). Leaf size: 49

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

\begin{align*} y &= -\frac {x^{3}}{4} \\ y &= c_1 x \left (c_1 +x \right ) \\ y &= c_1 x \left (c_1 -x \right ) \\ y &= c_1 x \left (c_1 -x \right ) \\ y &= c_1 x \left (c_1 +x \right ) \\ \end{align*}

✓ Mathematica. Time used: 1.31 (sec). Leaf size: 58

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

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

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (x*(-x**3 + 2*y(x)) + sqrt(x**5*(x**3 + 4*