68.4.3 problem 3

Internal problem ID [17183]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 3
Date solved : Thursday, October 02, 2025 at 01:49:42 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 21

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

\[ \frac {2 \sqrt {y}\, x -2 c_1 x +1}{2 x} = 0 \]

✓ Mathematica. Time used: 0.075 (sec). Leaf size: 25

ode=D[y[x],x]==Sqrt[y[x]]/x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.120 (sec). Leaf size: 19

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

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