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

` y=-(x+1)+ce^x`

Explanation

According to the question,


`(dy)/(dx)=x+x`


` (dy)/(dx)-y=x`


Comparing with `(dy)/(dx)+P y=Q`, we get


`P=-1, Q=x`


Now,`I.F =e^(int -1 d x)=e^(-x)`


So, the solution is given by


`y times I . F=int Q times I . F dx+c`


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