4.8.50 \(\sqrt {X} y'(x)+\sqrt {Y}=0\)

ODE
\[ \sqrt {X} y'(x)+\sqrt {Y}=0 \] ODE Classification

[_quadrature]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0029912 (sec), leaf count = 21

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

Maple
cpu = 0.006 (sec), leaf count = 15

\[ \left \{ y \relax (x ) =-{x\sqrt {Y}{\frac {1}{\sqrt {X}}}}+{\it \_C1} \right \} \] Mathematica raw input

DSolve[Sqrt[Y] + Sqrt[X]*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -((x*Sqrt[Y])/Sqrt[X]) + C[1]}}

Maple raw input

dsolve(diff(y(x),x)*X^(1/2)+Y^(1/2) = 0, y(x),'implicit')

Maple raw output

y(x) = -Y^(1/2)/X^(1/2)*x+_C1