choose the general solution of the differential equation dw/ds=5se^(7w)/4w

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`(dw)/(ds)=5se^(7w)/(4w)` ,

let us write this differential equation as variables are separable.

`(wdw)/e^(7w)=(5/4)sds` , integrating ,we get

 

`intwe^(-7w)dw=int(5/4)sds+ C`  ,

where c is integrating constant

`(we^(-7w))/(-7)+(1/7)e^(-7w)/(-7)=(5/4)s^2/2+c`

`-((w+1/7)e^(-7w))/7=(5/8)s^2+c`

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