84.5.14 problem 3.6

Internal problem ID [22101]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 3. Classification of first-order differential equations. Solved problems. Page 11
Problem number : 3.6
Date solved : Thursday, October 02, 2025 at 08:24:52 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=2 \sqrt {{| y|}} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 5

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

\[ y = 0 \]

✓ Mathematica. Time used: 0.144 (sec). Leaf size: 6

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

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

✓ Sympy. Time used: 0.122 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*sqrt(Abs(y(x))) + Derivative(y(x), x),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \int \limits ^{y{\left (x \right )}} \frac {1}{\sqrt {\left |{y}\right |}}\, dy = 2 x + \int \limits ^{0} \frac {1}{\sqrt {\left |{y}\right |}}\, dy \]