29.25.26 problem 723

Internal problem ID [5313]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 723
Date solved : Monday, January 27, 2025 at 11:08:30 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

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

\[ y \left (x \right )^{{3}/{2}}-x^{{3}/{2}}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 1.797 (sec). Leaf size: 21

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

\[ y(x)\to \left (x^{3/2}+\frac {3 c_1}{2}\right ){}^{2/3} \]