54.7.189 problem 1811 (book 6.220)

Internal problem ID [13038]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1811 (book 6.220)
Date solved : Wednesday, October 01, 2025 at 02:57:44 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} \sqrt {y}\, y^{\prime \prime }-a&=0 \end{align*}

✓ Maple. Time used: 0.035 (sec). Leaf size: 81

ode:=y(x)^(1/2)*diff(diff(y(x),x),x)-a = 0; 
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: 60.044 (sec). Leaf size: 1881

ode=-a + Sqrt[y[x]]*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ 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