Question

) Let F = xi + 2x À Find the particular parametrization of the flow line that goes through the point (4,5) and t = 0.

Answer 1

`x=4e^(t)\\y =8e^(t)+5`

Explanation:

Given that

`F = x\hat{i}+2x\hat{j}` --- (1)

with initial conditions

x(0) = 4 ; y(0) = 5

from given eq (1)

`x'(t)=x\\(1)/(x)dx=dt\\ln[x]=t+c_(1)\\x=Ce^(t)`

using initial condition at t = 0, x = 4

`4=Ce^(0)\\C=4`

`x=4e^(t)` ---- (2)

`y'(t)=2x\\y =2xt+B\\`

Using initial conditions:

`y =2xt+B`

⇒B = 5

`y =2(4e^(t))t+5\\y =8e^(t)+5`