29.25.26 problem 723

Internal problem ID [5313]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 723
Date solved : Sunday, March 30, 2025 at 07:53:36 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ y^{{3}/{2}}-x^{{3}/{2}}-c_1 = 0 \]

✓ Mathematica. Time used: 1.797 (sec). Leaf size: 21

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

\[ y(x)\to \left (x^{3/2}+\frac {3 c_1}{2}\right ){}^{2/3} \]

✓ Sympy. Time used: 4.655 (sec). Leaf size: 58

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

\[ \left [ y{\left (x \right )} = \left (C_{1} + x^{\frac {3}{2}}\right )^{\frac {2}{3}}, \ y{\left (x \right )} = \frac {\left (-1 + \sqrt {3} i\right ) \left (C_{1} + x^{\frac {3}{2}}\right )^{\frac {2}{3}}}{2}, \ y{\left (x \right )} = \frac {\left (-1 - \sqrt {3} i\right ) \left (C_{1} + x^{\frac {3}{2}}\right )^{\frac {2}{3}}}{2}\right ] \]