23.4.273 problem 273

Internal problem ID [6575]
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 : 273
Date solved : Friday, October 03, 2025 at 02:09:32 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.079 (sec). Leaf size: 17321

ode:=y(x)^(1/2)*diff(diff(y(x),x),x) = 2*b*x+2*a; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✗ Mathematica

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

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