Howtosignalprocessing
How do you find the transfer function of an ODE?
To find the transfer function, first take the Laplace Transform of the differential equation (with zero initial conditions). Recall that differentiation in the time domain is equivalent to multiplication by "s" in the Laplace domain. The transfer function is then the ratio of output to input and is often called H(s).
How do you calculate ODE?
Solution: Using the shortcut method outlined in the introduction to ODEs, we multiply through by dt and divide through by 5x−3: dx5x−3=dt. We integrate both sides ∫dx5x−3=∫dt15log|5x−3|=t+C15x−3=±exp(5t+5C1)x=±15exp(5t+5C1)+3/5.
