82.19.3 problem Ex. 3

Internal problem ID [18850]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IV. Singular solutions. problems at page 43
Problem number : Ex. 3
Date solved : Tuesday, January 28, 2025 at 12:28:58 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 16

dsolve(diff(y(x),x)*sqrt(x)=sqrt(y(x)),y(x), singsol=all)
 

\[ \sqrt {y \left (x \right )}-\sqrt {x}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.141 (sec). Leaf size: 26

DSolve[D[y[x],x]*Sqrt[x]==Sqrt[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

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