74.4.3 problem 3

Internal problem ID [15896]
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 : Tuesday, January 28, 2025 at 08:17:48 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x)=sqrt(y(x))/x^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.121 (sec). Leaf size: 25

DSolve[D[y[x],x]==Sqrt[y[x]]/x^2,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*}