67.1.8 problem 2.2 (h)

Internal problem ID [16273]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.2 (h)
Date solved : Thursday, October 02, 2025 at 10:45:14 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : solve: Cannot solve -8*x**2 + y(x)**2*Derivative(y(x), (x, 2))