The question asks to find the exact solution of the differential equation: y\' =

Question

The question asks to find the exact solution of the differential equation:

y' = x/(1+2y)

Given the initial condition y(-1) = 0.

I separated and then integrated, yielding the expression:

y+y2=0.5x + c I think it is impossible to solve this explicitly, so I believe there is some way I should manipulate the DE to get a separable expression that I can solve explicitly after integrating. y+y2=0.5x + c I think it is impossible to solve this explicitly, so I believe there is some way I should manipulate the DE to get a separable expression that I can solve explicitly after integrating.

Explanation / Answer

Actually, when you separate then integrate you get y + y^2 = (x^2)/2 + C. Then you use the initial values conditions y(-1) = 0 and plug them into the equation. So, you get 0 + 0^2 = (-1)^2 /2 + C. Therefore C = 1/2.

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