ODE
\[ \sqrt {X} y'(x)=\sqrt {Y} \] ODE Classification
[_quadrature]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.00303792 (sec), leaf count = 20
\[\left \{\left \{y(x)\to c_1+\frac {x \sqrt {Y}}{\sqrt {X}}\right \}\right \}\]
Maple ✓
cpu = 0.005 (sec), leaf count = 14
\[ \left \{ y \left ( x \right ) ={x\sqrt {Y}{\frac {1}{\sqrt {X}}}}+{\it \_C1} \right \} \] Mathematica raw input
DSolve[Sqrt[X]*y'[x] == Sqrt[Y],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), y(x),'implicit')
Maple raw output
y(x) = Y^(1/2)/X^(1/2)*x+_C1