What is the solution for t^{-1}(dy}{dt}=8cos^2(y),y(2)=\frac{3pi)/4 ?

The solution for t^{-1}(dy}{dt}=8cos^2(y),y(2)=\frac{3pi)/4 is y=arctan(4t^2-17)+pin

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t^{-1}(dy}{dt}=8cos^2(y),y(2)=\frac{3pi)/4

t^{- 1} \frac{d y}{d t} = 8 cos^{2} (y), y (2) = \frac{3 π}{4}

y = arctan (4 t^{2} - 17) + πn

Solution steps

t^{- 1} \frac{d y}{d t} = 8 cos^{2} (y)

Solve separable ODE:

y = arctan (4 t^{2} - 17) + πn

y = arctan (4 t^{2} - 17) + πn

y^{^{'}} + sin (y) = 0

\frac{d x}{d t} = - 9000 + \frac{7.5}{100} x

2 y y^{^{'}} = 9 t^{2}, y (0) = 2

x^{^{'}} = a + b \cdot x

sin (x) y^{^{'}} + \frac{sin ^{2} ( x )}{cos ( x )} y = 0

What is the solution for t^{-1}(dy}{dt}=8cos^2(y),y(2)=\frac{3pi)/4 ?
The solution for t^{-1}(dy}{dt}=8cos^2(y),y(2)=\frac{3pi)/4 is y=arctan(4t^2-17)+pin