Deriving expression for capacitor voltage

[Studious_stud]

Homework Statement

For the following circuit, obtain an expression for the capacitor
voltage, vC(t), for time, t (greater than or equal to) 0 if vs(t) = 10 V and vC(0) = 2 V.

Homework Equations

KVL
Definite integrals, differentiation etc

The Attempt at a Solution

Right so I can do this for a first order dynamic circuit (one with only one capacitor and one inductor) but this one is throwing me off.

I'd imagine you'd start by applying KVL to obtain an expression for the voltage source?

After that I'm kinda lost

Any help would be really appreciated thanks

 

[berkeman]

Homework Statement

For the following circuit, obtain an expression for the capacitor
voltage, vC(t), for time, t (greater than or equal to) 0 if vs(t) = 10 V and vC(0) = 2 V.

Homework Equations

KVL
Definite integrals, differentiation etc

The Attempt at a Solution

Right so I can do this for a first order dynamic circuit (one with only one capacitor and one inductor) but this one is throwing me off.

I'd imagine you'd start by applying KVL to obtain an expression for the voltage source?

After that I'm kinda lost

Any help would be really appreciated thanks

It looks like you just solve the circuit like the Vc(0) were zero, with a step input voltage at t=0 from the voltage source, but instead use Vc(0) = 2V as the initial condition instead. What is the issue?