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Determine which of the following differential equations is separable. (Select all that apply.) Determine which of the following differential equations is separable. (Select all that apply.) Find the solution to the differential equation below, subject to the given initial condition. dy / dx + y / 4 = 0, y(0) = 19 y(x) = Find the solution to the differential equation below, subject to the given initial condition. p dp / dt = 1, p(0) = 3 p(t) =

Explanation / Answer

1) Option 1 , 3 and 5

2) Option 1 , 3 and 4

3) dy/dx + y/4 = 0

dy/y = - dx/4

ln y = -x/4 + c

ln 19 = 0 + c

c = ln 19

y = 19e^(-x/4)

4) PdP = dt

0.5P^2 = t + c

0.5*9 = 0 + c

c = 4.5

P^2= 2t + 9

P(t) = sqrt(2t + 9 )

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