Posted by **Sara** on Sunday, July 7, 2013 at 3:38pm.

Find a general solution to the first – degree ODE. If an initial condition is given, find the corresponding particular solution. Write solution explicitly if possible.

(9x^2+y-1)dx-(4y-x)dy=0, y(1)=0

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**Steve**, Sunday, July 7, 2013 at 4:25pm
This is an exact equation. If

P(x,y) = 9x^2+y-1

Q(x,y) = x-4y

∂P/∂y = ∂Q/∂x

So, we have

3x^3 - x - 2y^2 + xy = c

Since y(1) = 0,

3 - 1 - 0 + 0 = c so c=2

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