Calculus-HELP PLZ !!!!

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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

  • Calculus-HELP PLZ !!!! -

    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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