ODE
\[ x y'(x)=4 \left (y(x)-\sqrt {y(x)}\right ) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0140277 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \left (e^{\frac {c_1}{2}} x^2+1\right ){}^2\right \}\right \}\]
Maple ✓
cpu = 0.006 (sec), leaf count = 15
\[ \left \{ -{x}^{2}{\it \_C1}+\sqrt {y \left ( x \right ) }-1=0 \right \} \] Mathematica raw input
DSolve[x*y'[x] == 4*(-Sqrt[y[x]] + y[x]),y[x],x]
Mathematica raw output
{{y[x] -> (1 + E^(C[1]/2)*x^2)^2}}
Maple raw input
dsolve(x*diff(y(x),x) = 4*y(x)-4*y(x)^(1/2), y(x),'implicit')
Maple raw output
-x^2*_C1+y(x)^(1/2)-1 = 0