- #1

Matthew R

- 7

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Thread moved from the technical PF forums so no Homework Help Template is shown

Hi guys.

I am currently stuck on the classic snow plow problem. I have the following differential equation and initial conditions:

@ 7am plow starts off to clear snow at a constant rate

By 8am, plow has gone 4mi

By 9am, plow has gone an additional 3mi

Let t=0 when it started to snow, when did it start to snow. They gave the answer as 4:27am

k(dx/dt)=1/t

It wants me to find the constant k.

Here is my work:

∫k dx= ∫dt/t

kx +C = ln (t) At this point I am assuming that x is the independent variable and t is the dependent variable.

e^(kx) +C = t

Using the first initial condition of when it starts to snow of x(0)=0, I get the C is 0, therefore

e^(kx) = t. Using the second initial condition @8, x(t+1)=4

e^(4k)= t+1.

This is the point I get stuck. I can't seem to solve for k that has a real number.

Any help would be appreciated.

I am currently stuck on the classic snow plow problem. I have the following differential equation and initial conditions:

@ 7am plow starts off to clear snow at a constant rate

By 8am, plow has gone 4mi

By 9am, plow has gone an additional 3mi

Let t=0 when it started to snow, when did it start to snow. They gave the answer as 4:27am

k(dx/dt)=1/t

It wants me to find the constant k.

Here is my work:

∫k dx= ∫dt/t

kx +C = ln (t) At this point I am assuming that x is the independent variable and t is the dependent variable.

e^(kx) +C = t

Using the first initial condition of when it starts to snow of x(0)=0, I get the C is 0, therefore

e^(kx) = t. Using the second initial condition @8, x(t+1)=4

e^(4k)= t+1.

This is the point I get stuck. I can't seem to solve for k that has a real number.

Any help would be appreciated.