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

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

[_quadrature]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.00386379 (sec), leaf count = 17

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

Maple
cpu = 0.006 (sec), leaf count = 13

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

DSolve[y'[x] == Sqrt[X*Y],y[x],x]

Mathematica raw output

{{y[x] -> x*Sqrt[X*Y] + C[1]}}

Maple raw input

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

Maple raw output

y(x) = (X*Y)^(1/2)*x+_C1