4.15.27 \(\sqrt {Y} y'(x)=\sqrt {X}\)

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

[_quadrature]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.00334414 (sec), leaf count = 20

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

Maple
cpu = 0.005 (sec), leaf count = 14

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

y(x) = X^(1/2)/Y^(1/2)*x+_C1