Differential Equation Involving Newtons Law of Motion

[SparkyEng]

Homework Statement

mv'=-gm-kv

Find the position function using the initial coniditions of t=0 for all Constants

Homework Equations

Reverse product rule

The Attempt at a Solution

My attempt is on my white board. Its attached as a picture.

 

[Dick]

Homework Statement

mv'=-gm-kv

Find the position function using the initial coniditions of t=0 for all Constants

Homework Equations

Reverse product rule

The Attempt at a Solution

My attempt is on my white board. Its attached as a picture.

You've got some problems there. For example the integral of vdt isn't equal to v*t. v is a function of t. Why don't you try to solve mv'=-gm-kv using separation of variables?

 

[HallsofIvy]

From mv'= m dv/dt= -gm- kv, you can get m dv/(gm+kv)= -dt, separating the variables "v" and "t". Integrate both sides of that.