77.1.81 problem 107 (page 162)

Internal problem ID [17900]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 107 (page 162)
Date solved : Monday, March 31, 2025 at 04:49:22 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} y^{\prime \prime }&=\frac {1}{\sqrt {y}} \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 65

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

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

✓ Mathematica. Time used: 60.051 (sec). Leaf size: 1471

ode=D[y[x],{x,2}]==1/Sqrt[y[x]]; 
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") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) - 1/sqrt(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out