23.2.6 problem 6

Internal problem ID [5361]
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 : 6
Date solved : Tuesday, September 30, 2025 at 12:36:10 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} {y^{\prime }}^{2}+3 x^{2}&=8 y \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 153

ode:=diff(y(x),x)^2+3*x^2 = 8*y(x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {3 x^{2}}{8}+\frac {\operatorname {RootOf}\left (\textit {\_Z}^{6}-18 \textit {\_Z}^{5} x +135 x^{2} \textit {\_Z}^{4}-540 \textit {\_Z}^{3} x^{3}+\left (1215 x^{4}-16 c_1 \right ) \textit {\_Z}^{2}+\left (-1458 x^{5}+32 c_1 x \right ) \textit {\_Z} +729 x^{6}-16 c_1 \,x^{2}\right )^{2}}{8} \\ y &= \frac {3 x^{2}}{8}+\frac {\operatorname {RootOf}\left (\textit {\_Z}^{6}+18 \textit {\_Z}^{5} x +135 x^{2} \textit {\_Z}^{4}+540 \textit {\_Z}^{3} x^{3}+\left (1215 x^{4}-16 c_1 \right ) \textit {\_Z}^{2}+\left (1458 x^{5}-32 c_1 x \right ) \textit {\_Z} +729 x^{6}-16 c_1 \,x^{2}\right )^{2}}{8} \\ \end{align*}

✓ Mathematica. Time used: 60.506 (sec). Leaf size: 1865

ode=(D[y[x],x])^2+3 x^2==8*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**2 - 8*y(x) + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -sqrt(-3*x**2 + 8*y(x)) + Derivative(y(x), x) cannot be solved b