How do you solve this simple differential equation?

[elcotufa]

Homework Statement

How would you solve

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


Thanks for your help

 

[LowlyPion]

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?

 

[elcotufa]

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?

 

[LowlyPion]

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