What is the solution for (dy)/(dx)+ycos(x)=6cos(x) ?

The solution for (dy)/(dx)+ycos(x)=6cos(x) is y=e^{-sin(x)+c_{1}}+6

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(dy)/(dx)+ycos(x)=6cos(x)

\frac{d y}{d x} + y cos (x) = 6 cos (x)

y = e^{- s i n (x) + c_{1}} + 6

Solution steps

\frac{d y}{d x} + y cos (x) = 6 cos (x)

Solve separable ODE:

y = e^{- s i n (x) + c_{1}} + 6

y = e^{- s i n (x) + c_{1}} + 6

e^{x} d x - (1 + e^{x}) y d y = 0

\frac{x ^{2}}{y ^{2} - 3} \frac{d y}{d x} = \frac{1}{2 y}

sin (x) cos (y) d x + cos (x) sin (y) d y = 0

3 x^{2} y^{2} \frac{d y}{d x} = 2 x - 1

\frac{d y}{d x} = \frac{2 x sin ^{2} ( y )}{( x ^{2} + 10 ) cos ( y )}

What is the solution for (dy)/(dx)+ycos(x)=6cos(x) ?
The solution for (dy)/(dx)+ycos(x)=6cos(x) is y=e^{-sin(x)+c_{1}}+6