4.15.27 $\sqrt{Y}{y}^{\prime }(x)=\sqrt{X}$

ODE
$$\sqrt{Y}{y}^{\prime }(x)=\sqrt{X}$$ ODE Classification

[_quadrature]

Book solution method
Separable ODE, Neither variable missing

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

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

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

$$\{y\left(x\right)=x\sqrt{X}\frac{1}{\sqrt{Y}}+\mathit{\_}\mathit{C}\mathit{1}\}$$ 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