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Calculus

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Solve the separable differential equation: dy/dt=4y^6
and find the particular solution satisfying the initial condition y(0)=-3

y(t)=?

  • Calculus -

    Integral of dt = Integral of (1/4)y^-6 dy

    t = -1/(20 y^-5) + C

    0 = 1/20*243 +C

    t = -1/(20 y^-5) -1/4860

    1/(20 y^-5) = -(1/4860) - t

    y^5 = (1/20)/[(-1/4860) - t]
    = 243/[-1 -4860 t]
    y = -3*[1 +4860 t]^(1/5)

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