4.4.45 \(x y'(x)=4 \left (y(x)-\sqrt {y(x)}\right )\)

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

\[ \left \{ -{x}^{2}{\it \_C1}+\sqrt {y \relax (x ) }-1=0 \right \} \] 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