How Can You Solve a Differential Equation Involving Exponential Drag Force?

[haruspex]

Are there any way to learn more calculus to get more strategy?

It looks like you need to reread integration basics, paying attention to bounds and to definite and indefinite integrals.

 

[ThEmptyTree]

I got v(t) = -1/c ln( e^(-c v_0) + bc/m t ).

 

[haruspex]

I got v(t) = -1/c ln( e^(-c v_0) + bc/m t ).

Good.

 

[idekthanks]

Homework Statement:: MIT pretest.
Relevant Equations:: 𝐅⃗=−𝑏𝑒^(𝑐𝑣)𝐢̂ , find v(t), by using differential equation of F=maHello, would you mind sharing what course this is? I am familiar with edx but can’t find it

 

[haruspex]

@idekthanks , the thread is over a year old. @MichaelTam might not be visiting the forum any more.

 

[deepread]

@idekthanks Maybe this is a late reply, but I leave it for future readers.
The course contents are available here - https://ocw.mit.edu/courses/8-01sc-classical-mechanics-fall-2016/

 

[Delta2]

This problem becomes more complex if we alter the initial condition of $v_0$ to be not parallel to x-axis but to have some other direction. For example if $v_0$ is in the y-axis then the differential equation becomes $$m\frac{dv_x}{dt}=-be^{c\sqrt{v_0^2+v_x^2}}$$ and who can solve this