Solve the differential equation: `(dy)/(dx)+5y=cos4x`

Explanation

It is given that

`frac{d y}{d x}+5 y=\cos 4 x \ldots .(1)`

Clearly, it is a linear differential equation of the form

`frac{d y}{d x}+P y=Q`

where `P=15` and `Q=\cos 4 x`

`=e^{\int 5 d x} `

`=e^{5 x}`

`\therefore I . F_{*}=e^{\int P d x}`

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