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

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

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