29.31.7 problem 906

Internal problem ID [5486]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 906
Date solved : Sunday, March 30, 2025 at 08:17:14 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.196 (sec). Leaf size: 49

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

\begin{align*} y &= -2 x^{{3}/{2}} \\ y &= 2 x^{{3}/{2}} \\ y &= \frac {x \left (c_1^{2}+4 x \right )}{2 c_1} \\ y &= \frac {x \left (c_1^{2} x +4\right )}{2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 60.321 (sec). Leaf size: 961

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (sqrt(-4*x**3 + y(x)**2) + 3*y(x))/(2*x) cannot be solved by the factorable group method