23.1.100 problem 99

Internal problem ID [4707]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 99
Date solved : Tuesday, September 30, 2025 at 08:15:49 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

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

\[ x +2 \left (\left \{\begin {array}{cc} \sqrt {-y} & y\le 0 \\ -\sqrt {y} & 0<y \end {array}\right .\right )+c_1 = 0 \]

✓ Mathematica. Time used: 0.112 (sec). Leaf size: 31

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

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\sqrt {| K[1]| }}dK[1]\&\right ][x+c_1]\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.117 (sec). Leaf size: 14

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

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