How do you solve this simple differential equation?

AI Thread Summary
To solve the differential equation 2 = v(t)/10 + (1/2)∫v(t)dt, the equation can be rearranged to isolate the integral. The solution involves recognizing that the resulting function resembles an exponential decay, specifically 20e^(-5t). The general solution format is A + Bexp(-kt), where A is zero in this case. The value of B can be challenging to determine without initial conditions. The discussion emphasizes the need for differentiation to eliminate the integral for a clearer solution path.
elcotufa
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Homework Statement



How would you solve

2=\frac{v(t)}{10}+\frac{\int{v(t)}}2


Thanks for your help
 
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elcotufa said:

Homework Statement



How would you solve

2=\frac{v(t)}{10}+\frac{\int{v(t)}}2


Thanks for your help

Try rearranging the equation.

\int{v_{(t)} = 4 - \frac{v_{(t)}}{5}

What function do you know that will yield this kind of result?
 
I know the answer is 20e^(-5t) by just taking the 1/10 out from the v(t), and the k on top of the exponential is negative 10/2 but I don't know the solving mechanismMy calc book only has one example and it is when it equals a function and not a constant in the first equation, so I can just differentiate the equation to get rid of the integral

The answer should be in the form A+Bexp(-kt)
A is zero for this equation but can I find B without any initial conditions?
 
elcotufa said:
I know the answer is 20e^(-5t) by just taking the 1/10 out from the v(t), and the k on top of the exponential is negative 10/2 but I don't know the solving mechanism


My calc book only has one example and it is when it equals a function and not a constant in the first equation, so I can just differentiate the equation to get rid of the integral

The answer should be in the form A+Bexp(-kt)
A is zero for this equation but can I find B without any initial conditions?

\int{v_{(t)} = 4 - \frac{v_{(t)}}{5}

Taking the common integral of e you can start with this

\int{e^{(ct)} = \frac{e^{ct}}{c}

http://en.wikipedia.org/wiki/List_of_integrals_of_exponential_functions
 
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