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  4. If the I.F. of the differential equation ( dy / dx )+5 y = cos x is ∫ e Adx , then A =

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Q. If the I.F. of the differential equation $\frac{ dy }{ dx }+5 y =\cos x$ is $\int e ^{ Adx }$, then $A =$

Differential Equations

Solution:

The I.F. of the differential equation
$\frac{ dy }{ dx }+ Py = Q$ is $e ^{\int Pdx} .$
Here $P =5$
therefore $I.F. = e ^{\int 5 dx } .$
Hence $A =5$.