85.7.8 problem 1 (h)

Internal problem ID [22462]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 32
Problem number : 1 (h)
Date solved : Thursday, October 02, 2025 at 08:40:06 PM
CAS classification : [[_homogeneous, `class G`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 5

ode:=diff(y(x),x) = (x*y(x))^(1/2); 
ic:=[y(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 6

ode=D[y[x],{x,1}]==Sqrt[x*y[x]]; 
ic={y[1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.310 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt(x*y(x)) + Derivative(y(x), x),0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x^{3}}{9} - \frac {2 \sqrt {x^{3}}}{9} + \frac {1}{9} \]