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# Solving differential equations

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a. Derive an ODE (in standard form) for the current at the voltage source.

B. Solve the ODE from question 1, given $${V}_{s}(t) = 12t$$

Mar 19, 2018

### 2+0 Answers

#1
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I'm confident i've got the correct ODE. (part a)

$$\frac{di}{dt} + \frac{1}{RC}i = \frac{d{V}_{s}}{dt}\frac{1}{R}$$

I come unstuck with part b

I'm not sure how to solve it with a $${V}_{s}(t) = 12t$$

If I use the non homogeneous methord to solve it,

I get a $${y}_{H} = i(t) ={C}_{1}{e}^{-\frac{1}{RC}t}$$

and then I don't know what my guess is for the RHS = $$\frac{d{V}_{s}}{dt}\frac{1}{R}$$

have I got the incorrect ODE in the first place?

any help is greatly appreciated!!

Mar 19, 2018
#2
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came up with another go for it...no idea if it's correct.

Mar 19, 2018

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