29.14.25 problem 406

Internal problem ID [5004]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 14
Problem number : 406
Date solved : Monday, January 27, 2025 at 10:02:40 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

\[ y \left (x \right ) = \frac {\sqrt {Y}\, x}{\sqrt {X}}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 20

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

\[ y(x)\to \frac {x \sqrt {Y}}{\sqrt {X}}+c_1 \]