71.2.4 problem 4

Internal problem ID [14336]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises 1.3, page 27
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 06:26:54 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

dsolve(diff(y(x),x)=x*y(x)^(1/2),y(x), singsol=all)
 

\[ \sqrt {y}-\frac {x^{2}}{4}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.118 (sec). Leaf size: 24

DSolve[D[y[x],x]==x*y[x]^(1/2),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{16} \left (x^2+2 c_1\right ){}^2 \\ y(x)\to 0 \\ \end{align*}