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Find the general solution for the following differential equat

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Find the general solution for the following differential equation. $(x + y + 1) \frac{d y}{d x} = 1$

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Find the general solution for the following differential equation.

(x + y + 1) \frac{d y}{d x} = 1

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Text solutionVerified

(x + y + 1) \frac{d y}{d x} = 1

\frac{d x}{d y} - x = (y + 1)

= e^{- \int d y} = e^{- y}

x \times e^{- y} = \int (y + 1) e^{- y} d y + C

= \int I y II e^{- y} d y + \int e^{- y d y} + C

= - y e^{- y} + 2 \int e^{- y} d y + C

= - y e^{- y} - 2 e^{- y} + C

∴ x = C e^{y} - (y + 2)

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Question Text	Find the general solution for the following differential equation. $(x + y + 1) \frac{d y}{d x} = 1$
Answer Type	Text solution:1
Upvotes	150