29.14.24 problem 405

Internal problem ID [5003]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 14
Problem number : 405
Date solved : Monday, January 27, 2025 at 10:02:39 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime } \sqrt {X}+\sqrt {Y}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

dsolve(diff(y(x),x)*sqrt(X)+sqrt(Y) = 0,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: 21

DSolve[D[y[x],x] Sqrt[X]+Sqrt[Y]==0,y[x],x,IncludeSingularSolutions -> True]
 

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