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$The general solution of the D.E y^{1} + y φ^{1} (x) - φ (x) φ^{1} (x) = 0 where φ (x) is a known function in$

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y=ce-φ(x)+φ(x)-1

y=ceφ(x)+φ(x)-1

y=ce-φ(x)-φ(x)+1

y=ce-φ(x)+φ(x)+1

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detailed solution

Correct option is A

dydx+yφ1(x)=φ(x)φ1(x)I⋅F=e∫φ′(x)dx=eφ(x) Solution of the D.E. yeφ(x)=∫eφ(x)⋅φ(x)φ1(x)dx yeφ(x)=∫et⋅tdt=et(t−1)+c yeφ(x)= eφ(x)φ(x)-1+cy=ce−φ(x)+φ(x)−1

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The general solution of the D.E y1+yφ1(x)−φ(x)φ1(x)=0 where φ(x) is a known function in

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$The general solution of the D.E y^{1} + y φ^{1} (x) - φ (x) φ^{1} (x) = 0 where φ (x) is a known function in$