# Math Help - 1st order ODE help

1. ## 1st order ODE help

T'= k1*exp(k2*t) - k3(T-T0)

determine T(t), assume that T(-infinity)= T0

2. What have you tried so far?

3. I assume this is

$\frac{dT}{dt} = k_1e^{k_2t} - k_3(T - T_0)$

$\frac{dT}{dt}= k_1e^{k_2t} - k_3T + k_3T_0$

$\frac{dT}{dt} + k_3T = k_1e^{k_2t} + k_3T_0$

This is first order linear, so now use the Integrating Factor method.

4. I had tried substitution to no avail. Hadn't used the integrating factor method, I'm quite amazed at how easy it is to use. Thanks for your help