23.4.272 problem 272

Internal problem ID [6574]
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 : 272
Date solved : Tuesday, September 30, 2025 at 03:07:54 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} \sqrt {y}\, y^{\prime \prime }&=a \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 81

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

\begin{align*} \frac {\left (-2 a \sqrt {y}-c_1 \right ) \sqrt {4 a \sqrt {y}-c_1}-6 a^{2} \left (x +c_2 \right )}{6 a^{2}} &= 0 \\ \frac {\left (2 a \sqrt {y}+c_1 \right ) \sqrt {4 a \sqrt {y}-c_1}-6 a^{2} \left (x +c_2 \right )}{6 a^{2}} &= 0 \\ \end{align*}

✓ Mathematica. Time used: 60.041 (sec). Leaf size: 1881

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

Too large to display

✗ Sympy

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

Timed Out