1)Consider the simplest linear model of the increment \DeltaT to the Earth’s mean surface temperature arising from a forcing \DeltaQ and a feedback factor, \lambda:
C. \frac {d Delta T}{dt} + \lambda \DeltaT = \DeltaQ
where C is the effective heat capacity of the climate system. Assume a linearly increasing radiative forcing, \DeltaQ = b.t, where t is the time in years from 1850.

a)Write-down an equation for the equilibrium temperature change that would arise from stabilising forcing at each time t.
b) Assuming \DeltaT=0at t=0, solve the simplest linear model equation to give the dynamical temperature change as a function of t, C, \lambda and b.

I can do a) and i get
\Delta T_{eq}= b.t/ \lambda

i try b) and i get \Delta T_{cf}=A \exp^{\frac{- \lambda.t}{c}}

and T_{pi}=B.b.t therefore giving me CBb+ \lambdaBbt=bt

therefore \Delta T= A \exp ^{\frac{- \lambda.t}{c}} + \frac {bt^{2}}{C+\lambda . t}

and \Delta T =0 and t=0
Therefore A = 0

Therefore i get \Delta T = \frac {bt^{2}}{C+\lambda . t}

if any one could shed any light that would be useful