23.4.238 problem 238

Internal problem ID [6540]
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 : 238
Date solved : Tuesday, September 30, 2025 at 03:03:59 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]^2 + y[x]^2*D[y[x],{x,2}] == a + b*x; 
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 - b*x + y(x)**2*Derivative(y(x), (x, 2)) + y(x)*Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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