Given $K(0) = 0,\!2P$. I'm supposed to solve the ODE
$$ \frac{dK}{dt} = \lambda(P-K)$$
I have tried to seperate and integrate both sides
$$ \int \frac{1}{P-K} dK = \int \lambda \space dt$$
to get
$$\ln(P-K) = \lambda t + C$$
and then solve for $K$
$$ e^{\ln(P-K)} = P-K=e^{\lambda t + C}$$ $$ -(-K) = -(-P + e^{\lambda t + C})$$ $$ K = P - e^{\lambda t + C}$$
is that about right for the general solution? And where I'm really stuck is how do I proceed to find the particular solution?