$$ \frac{\dot{c_t}}{c_t}=f'(k_t)-\delta-\sigma $$ $$ \dot k_t =f(k_t)-c_t-(n+\delta)k_t$$ $$(\delta,\,\sigma \text{ and } n \text{ are parameters}, \, c_t=c(t),\, k_t=k(t)) $$

How can I solve this differential equation?

Is it okay to solve the equations with multiplying integrating factor in both side? $\frac{dy}{dt}+p(t)y=q(t)$

Any hints please?



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