82.19.4 problem Ex. 4

Internal problem ID [18780]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IV. Singular solutions. problems at page 43
Problem number : Ex. 4
Date solved : Monday, March 31, 2025 at 06:12:37 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.276 (sec). Leaf size: 49

ode:=x^2*diff(y(x),x)^2-3*x*y(x)*diff(y(x),x)+2*y(x)^2+x^3 = 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: 60.311 (sec). Leaf size: 961

ode=x^2*D[y[x],x]^2-3*x*y[x]*D[y[x],x]+2*y[x]^2+x^3==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