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`v = 1/(y^(n))`` v = 1/(y^(n-1))`` v = y^(n)``v = y^(n-1)`

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aSolution :

The Given differential equation is <br> ` (dy)/(dx) + P (x)* y = Q (x) * y^(n)` <br> ` rArr 1/(y^(n)) * (dy)/(dx) + y^(-n+1) P y = Q (x)* y^(n)` <br> Put ` 1/(y^(n-1))= v ` <br> ` rArr (-n +1) y^(-n)(dy)/(dx) =(dv)/(dx)` <br> ` :. 1/(-n+1) * (dv)/(dx) +P (x) * v = Q (x)` <br> ` rArr (dv)/(dx) +(1-n) P (x) * v = (1-n) Q (x)` <br> which is linear differential equation . <br> Hence , required substitiution is ` v = 1/(y^(n-1))`