23.4.101 problem 101

Internal problem ID [6403]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 4. THE NONLINEAR EQUATION OF SECOND ORDER, page 380
Problem number : 101
Date solved : Tuesday, September 30, 2025 at 02:56:19 PM
CAS classification : [NONE]

\begin{align*} 2 x y+a \,x^{4} {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=b \end{align*}

✗ Maple

ode:=2*x*y(x)+a*x^4*diff(y(x),x)^2+x^2*diff(diff(y(x),x),x) = b; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

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