85.31.2 problem 6

Internal problem ID [22622]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. B Exercises at page 64
Problem number : 6
Date solved : Thursday, October 02, 2025 at 08:55:14 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 14

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

\[ \sqrt {y}-\frac {x}{2}-c_1 = 0 \]

✓ Mathematica. Time used: 0.062 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to \frac {1}{4} (x+c_1){}^2\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.105 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = \frac {C_{1}^{2}}{4} + \frac {C_{1} x}{2} + \frac {x^{2}}{4} \]