Hi Guys, I just started DE so I am at first unit. Has anyone looked at problem set part I problem no. 7
I am comparing my setup with the solution. I got the right hand side right which in solution is some constant (rate at which snowplow clears snow) time delta time giving the volume of snow cleared in cubic meters.
MIT 18.03SC Differential Equations
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I had to post the remaining part of the question as comment due to characters limit.
The problem I have is setting up the right hand side. At some time t starting at t=0 the height of snow is k1 (meters/hours) times t. Now I have k1*t and I know somehow delta x is related to the volume it digs through the snow. But I have it written down on the left side but don't have a clue how I will equate two sides of the solution. The solution says to equate delta x*k1*t and the volume of snow k2*delta t but the units don't match up. Left hand side has units of squared meters.
http://ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011/unit-i-first-order-differential-equations/basic-de-and-separable-equations/MIT18_03SCF11_ps1_s1q.pdf the correct link. I am not sure why the earlier one did not work.
Ok, I might have answered my question. I can introduce a width factor in my LHS, which gives me volume snowplow dug through and also makes the equation agree unit wise but that is just introducing constant and the resultant DE will be equivalent to what the solution says. I hope the solution made it much more clear.
If anyone has a different approach please suggest me too.