What is the solution for 2sqrt(x)y^'=cos^2(y),y(0)=2 ?

The solution for 2sqrt(x)y^'=cos^2(y),y(0)=2 is y=arctan(sqrt(x)+tan(2))+pin

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2sqrt(x)y^'=cos^2(y),y(0)=2

2 x y^{^{'}} = cos^{2} (y), y (0) = 2

y = arctan (x + tan (2)) + πn

Solution steps

2 x y^{'} (x) = cos^{2} (y)

Solve separable ODE:

y = arctan (x + tan (2)) + πn

y = arctan (x + tan (2)) + πn

\frac{d y}{d x} = \frac{2 x}{- 8 y - 6}

\frac{d y}{d x} = (y^{2} x)

2 y y^{^{'}} = 1, y (0) = x - 1

a (y) \frac{d y}{d t} = - a 2 g y

\frac{d y}{d x} = \frac{3 x ^{2} - 6 x ^{2} y ^{2}}{y - x ^{3} y}

What is the solution for 2sqrt(x)y^'=cos^2(y),y(0)=2 ?
The solution for 2sqrt(x)y^'=cos^2(y),y(0)=2 is y=arctan(sqrt(x)+tan(2))+pin