ODE
\[ y'(x)=\text {R1}\left (x,\sqrt {X}\right ) \text {R2}\left (y(x),\sqrt {Y}\right ) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.226185 (sec), leaf count = 43
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\text {R2}\left (K[1],\sqrt {Y}\right )}dK[1]\& \right ]\left [\int _1^x\text {R1}\left (K[2],\sqrt {X}\right )dK[2]+c_1\right ]\right \}\right \}\]
Maple ✓
cpu = 0.036 (sec), leaf count = 26
\[\left [\int \mathit {R1} \left (x , \sqrt {X}\right )d x -\left (\int _{}^{y \left (x \right )}\frac {1}{\mathit {R2} \left (\textit {\_a} , \sqrt {Y}\right )}d \textit {\_a} \right )+\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[y'[x] == R1[x, Sqrt[X]]*R2[y[x], Sqrt[Y]],y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[Inactive[Integrate][R2[K[1], Sqrt[Y]]^(-1), {K[1], 1, #1}] & ][C[1] + Inactive[Integrate][R1[K[2], Sqrt[X]], {K[2], 1, x}]]}}
Maple raw input
dsolve(diff(y(x),x) = R1(x,X^(1/2))*R2(y(x),Y^(1/2)), y(x))
Maple raw output
[Int(R1(x,X^(1/2)),x)-Intat(1/R2(_a,Y^(1/2)),_a = y(x))+_C1 = 0]