# Not sure if my calculation is correct, can anyone check this RC circuit for me?

Hello everyone, so in my book I decided to do this practice question but failed to notice that the answer was not given in the back of the book. If anyone can help me confirm my answer I would much appreciate it.

The problem asks me to find the current over the 5 ohm resistor as a function of time. The initial condition is that the capacitor is charged to 5 volts. Top of the capacitor is positive polarity bottom is negative; should have put the signs in.

The answer I got to was the following:

$$i_{R_{(5\Omega)}}(t)=\frac{(20sin(4t))}{(241)} + \frac{75cos(4t)}{241} + \frac{10}{3} - 2.6445e^{(-15t)}$$

If the formatting of this post is all wrong please forgive me. This is the first post I've ever made on a stackexchange site!

The INCORRECT Work I did to get to the answer above