74.1.6 problem 9

Internal problem ID [15715]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 9
Date solved : Monday, March 31, 2025 at 01:45:52 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

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