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# Find the equation of 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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Toolbox:
• $\large\frac{dy}{dx}$ is the slope of the curve.
• If the given equation is a first order linear equation, to solve this:
• (i) Write the given equation in the form of $\large\frac{dy}{dx}$$+ Py = Q • (ii) Find the integrating factor (I.F) = e^{\int Pdx}. • (iii) Write the solution as y(I.F) = integration of Q(I.F) dx + C Step 1: With the given information: Let the curve be F(x,y) and \large\frac{dy}{dx} be the slope. Hence the equation is \large\frac{dy}{dx }$$ = x + y$

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