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Q.The solution of dydx+y=1+x+x2+x3+⋯+xn\dfrac{dy}{dx} + y = 1 + x + x^2 + x^3 + \cdots + x^n is

a
y=e−x∫ex(xn+1−1x−1)dx+Ce−xy = e^{-x} \int e^x (\dfrac{x^{n+1} - 1}{x-1}) dx + C e^{-x}
b
y=e−x∫ex(1−xn+11−x)dx+Ce−xy = e^{-x} \int e^x (\dfrac{1 - x^{n+1}}{1-x}) dx + C e^{-x}
c
y=ex∫e−x1−xn+11−xdx+Cexy = e^x \int e^{-x} \dfrac{1 - x^{n+1}}{1-x} dx + C e^x
d
y=1−xn+11−x+Cy = \dfrac{1 - x^{n+1}}{1-x} + C

Correct Answer: Option B

The correct solution involves applying the fundamental concept to derive the final value step by step...

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