First off, I apologize for the lack of information in the title, I had to shorten it due to the 150 character limit.
The question I am attempting can be seen here:
$ e_{gen}$ , $k$, $\rho$ (density) , and $ c $ (specific heat capacity) are constant with respect to distance, $x$, and time, $t$
$ \frac{ \partial}{\partial{x}} \left( k \frac{\partial{T}}{\partial{x}} \right) + e_{gen} = \rho c \frac{\partial{T}}{\partial{t}} $
Show how under steady state conditions, this equation reduces to $$ \frac{d^2T}{dx^2} + \frac{e_{gen}}{k} = 0 $$
Honestly I'm at a loss as to how to tackle this question. I have searched for examples to base it off and I can't fully grasp what to do.
Also, I am unsure if I integrated the other questions on the question sheet correctly. I did do the other questions, and the answers match up with the solutions, but I don't know if my method was correct or if I kinda brute forced it to look right, without actually using the correct method.
My solution to the third question can be seen in the image below, with a separate image containing the questions.
Under steady state conditions, $T$ is constant with respect to time. So $\partial_t T = 0$, and your equation becomes $$ \frac{d}{dx}( \kappa \frac{d}{dx} T) + e_{gen} = 0 $$ Since $\kappa$ is constant (and non-zero), then pull $\kappa$ out of the differentiation, divide through by $\kappa$ to get $$ \frac{d^2}{dx^2} T + \frac{e_{gen}}{\kappa}=0. $$