text: Ok, the characteristic equation is\nλ² + 16λ + 0 = 0\nThe roots are\nλ = 0, -16\nThe characteristic roots are\ne^0, e^(-16x)\n\nThe solution to the diff. eq. is of the form:\nAe^(-16x) + B\n\nPlug in the initial values:\nAe^(-16*0) + B = -5 => B = -5\nAe^(-16π/8) - 5 = 7 => A = 12/e^(-2π), approximately 6425.9\n\nYour final solution is:\n12e^(-16x - 2π) - 5