Internal problem ID [12600]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 1. Introduction. Exercises 1.3, page 27
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-x \sqrt {y}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x)=x*y(x)^(1/2),y(x), singsol=all)
\[ \sqrt {y \left (x \right )}-\frac {x^{2}}{4}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.2 (sec). Leaf size: 24
DSolve[y'[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*}