Add family payment method4/21/2023 ![]() Then, find a function μ, such that when we multiply the equation by this μ(t) the left hand side becomes a full derivative of the function μ(t) y(t) (a) First, collect all the y terms to the left hand side (LHS). This new method will be much more useful when we deal with first order linear differential equations where can't clearly see a way to assume a certain form for the solution that simplifies the problem. We could also solve this equation without assuming that the solution is of the form y(t)=e^t u(t). (b) Solve the equation terms of u and find the answer to your original model by writing y(t)=e^t u(t).ģ. Then plug this into the equation and write a new differential equation in terms of the function u. (a) Assume first that the solution is of the form y(t)=e^t u(t). One way of solving this problem is to exploit the properties of the equation. We see that this equation is neither autonomous nor separable. Where g(t)=e^t is the rate at which we are harvesting.Ģ. Suppose that our new model for the population is ![]() Now, assume that to make sure that our population doesn't grow too much we harvest/remove some of the population at a certain time-dependent rate. Here the k>0 term represents the proportionality constant. SOLVED: We know that with ample space and food resources, the rate of change of the population of a species may, at least for a while, be proportional to the population.
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