What is the solution for ((dy))/((dt))=2tcos^{(2)}(y) ?

The solution for ((dy))/((dt))=2tcos^{(2)}(y) is y=arctan(t^2+c_{1})+pin

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((dy))/((dt))=2tcos^{(2)}(y)

\frac{( d y )}{( d t )} = 2 t cos^{(2)} (y)

y = arctan (t^{2} + c_{1}) + πn

Solution steps

\frac{( d y )}{( d t )} = 2 t cos^{(2)} (y)

Solve separable ODE:

y = arctan (t^{2} + c_{1}) + πn

y = arctan (t^{2} + c_{1}) + πn

(x^{2} + 4) \frac{d y}{d x} + x y = 2 x, y (0) = 3

\frac{d x}{d t} = x sin (t), x (0) = 3

x y^{^{'}} = \frac{3 y ^{3} + 12 y x ^{2}}{2 y ^{2} + 8 x ^{2}}

\frac{d y}{d x} = x y + 6 x + 3 y + 18

y^{^{'}} - 4 y^{2} e^{- 4 x} = 0, y (0) = 4

What is the solution for ((dy))/((dt))=2tcos^{(2)}(y) ?
The solution for ((dy))/((dt))=2tcos^{(2)}(y) is y=arctan(t^2+c_{1})+pin