Thread: Separation of Variables

i need help with a problem involving separation of variables. here's the entire problem:

let v(t) be the velocity, in feet per second, of a skydiver at time t seconds, t > or = 0. after her parachute opens, her velocity satisfies the differential equation dv/dt = -2v - 32, with initial condition v(0) = -50

use separation of variables to find an expression for v in terms of t, where t is measured in seconds

anyone mind helping out?

Originally Posted by junkedly

i need help with a problem involving separation of variables. here's the entire problem:

let v(t) be the velocity, in feet per second, of a skydiver at time t seconds, t > or = 0. after her parachute opens, her velocity satisfies the differential equation dv/dt = -2v - 32, with initial condition v(0) = -50

use separation of variables to find an expression for v in terms of t, where t is measured in seconds

anyone mind helping out?

hi jun

, then



solve this differential equation

Now integrate both sides.

thanks for the quick replies

i had that much so far, but i when i integrate dv/-2v-32 i get an antiderivative that is a nonreal answer

i end up with -2ln(-2v - 32) = t, but then the initial condition doesn't work because a natural logarithm can't equal zero

thanks again for the help

finish ...

a huuuuuge thank you skeeter

i always manage to overlook possible factoring

you saved me

so adding the initial conditions of v(0) = -50 i get


ln|-50+16| = -2(0) + C

C = 3.526

therefore ln|v+16| = -2t + 3.526

does this look correct?

Originally Posted by junkedly

so adding the initial conditions of v(0) = -50 i get


ln|-50+16| = -2(0) + C

C = 3.526

therefore ln|v+16| = -2t + 3.526

does this look correct?

... let





...

finish