89.30.28 problem 30

Internal problem ID [24945]
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 : 30
Date solved : Thursday, October 02, 2025 at 11:36:24 PM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Maple. Time used: 0.060 (sec). Leaf size: 153

ode:=8*y(x) = 3*x^2+diff(y(x),x)^2; 
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: 60.279 (sec). Leaf size: 1865

ode=8*y[x]==3*x^2+D[y[x],x]^2; 
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