Consider a causal LTI system characterized by differential equation \(\frac{{dy\left( t \right)}}{{dt}} + \frac{1}{6}y\left( t \right) = 3x\left( t \right)\). The response of the system to the input \(x\left( t \right) = 3{e^{ - \frac{t}{3}u\left( t \right)}}\). Where u(t) denotes the unit step function is

• A. \(9{e^{ - \frac{t}{3}}}u\left( t \right)\)
• B. \(9{e^{ - \frac{t}{6}}}u\left( t \right)\)
• C. \(9{e^{ - \frac{t}{3}}}u\left( t \right) - 6{e^{ - \frac{t}{6}}}u\left( t \right)\)
• D. \({54^{ - \frac{t}{6}}}u\left( t \right) - 54{e^{ - \frac{t}{3}}}u\left( t \right)\)