89.30.2 problem 4

Internal problem ID [24919]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 16. Equations of order one and higher degree. Exercises at page 243
Problem number : 4
Date solved : Thursday, October 02, 2025 at 10:49:38 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} {y^{\prime }}^{2}+4 x^{4} y^{\prime }-12 x^{4} y&=0 \end{align*}

✗ Maple

ode:=diff(y(x),x)^2+4*x^4*diff(y(x),x)-12*x^4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]^2+4*x^4*D[y[x],x]-12*x^4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*x**4*y(x) + 4*x**4*Derivative(y(x), x) + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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