Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

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Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

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Text solutionVerified

According to question, we have

\frac{d y}{d x} = x + y

\frac{d y}{d x} - y = x

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

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Question Text	Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.
Answer Type	Text solution:1
Upvotes	150

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

Text solutionVerified

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