Electric Circuit Differential equation help

[Vossi]

Homework Statement

See attached image

Relevant Equations

First Order Differential equation for electrical circuit

I'm confused at the part how 4Vc and 48 cos(60t) are deduced, that's all.

 

[berkeman]

Welcome to PhysicsForums.

Homework Statement:: See attached image
Relevant Equations:: First Order Differential equation for electrical circuit

I'm confused at the part how 4Vc and 48 cos(60t) are deduced, that's all.

It looks like they are just giving the equation for one case of the values of R, C and the driving voltage source...

 

[Mark44]

I'm confused at the part how 4Vc and 48 cos(60t) are deduced, that's all.

I don't get it, either.
The units for R and C should be in ohms and farads, so $RC = (2 \times 10^3)(5 \times 10^{-6}) = 10 \times 10^{-3} = 10^{-2}$ ohms-farads.
It's possible there is a mistake in the published answer.

 

[DaveE]

Yes, clearly RC=0.25 sec for the answer given. Like 50Kohm & 5uF, for example.