14.17 problem 398

Internal problem ID [3144]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 14
Problem number: 398.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_quadrature]

Solve \begin {gather*} \boxed {y^{\prime } \sqrt {X}-\sqrt {Y}=0} \end {gather*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

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

Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 20

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

\begin{align*} y(x)\to \frac {x \sqrt {Y}}{\sqrt {X}}+c_1 \\ \end{align*}