Initial Value Problems Calculus

Calculus problem how do you do it?

Solve the initial-value problem. dx/dt + 2tx = x , x(0)=5. Use your solution to compute x(3). Please show work and how do you do it?

Rearrange to dx/dt = x – 2tx
dx/dt = x(1 – 2t)

split & integrate
Int 1/x dx = Int (1-2t) dt
ln|x| = t – t^2 + c
x(0)=5 ? are you actually saying that when t = 0, x = 5 (this makes more sense)
assuming this is the case:
ln5 = c

so ln|x| = t – t^2 + ln5

t = 3: ln|x| = 3 – 9 + ln5 = -6 + ln5
x = e^(-6 + ln5) = 0.012

Initial Value Problem Example 1