What is the solution for y^'+ycos(x)=5cos(x),y(0)=7 ?

The solution for y^'+ycos(x)=5cos(x),y(0)=7 is y=2e^{-sin(x)}+5

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y^'+ycos(x)=5cos(x),y(0)=7

y^{^{'}} + y cos (x) = 5 cos (x), y (0) = 7

y = 2 e^{- s i n (x)} + 5

Solution steps

y^{'} (x) + y cos (x) = 5 cos (x)

Solve separable ODE:

y = 2 e^{- s i n (x)} + 5

y = 2 e^{- s i n (x)} + 5

x \to 1 - lim (3 x - 5)

\int x (- 1 + x^{2}) d x

x \to 0 lim (\frac{4 x - sin ( x )}{x})

\int e^{y} y^{2} d y

\frac{\partial}{\partial x} (9 x e^{x + y})

What is the solution for y^'+ycos(x)=5cos(x),y(0)=7 ?
The solution for y^'+ycos(x)=5cos(x),y(0)=7 is y=2e^{-sin(x)}+5