Handwritten solving. 3 Euler's solver (#differentiation, #integration)Consider a differential equation of the typedydt(1)where f is a function that may depend on both t and y. We want to find the solutionto this differential equation, y(t), with initial conditions prescribed by y(to) = yo. Ourgoal in this problem is to derive a computational scheme known as Euler's method, andsee how it can be useful to approximate solutions to first-order differential equations.= f(t, y),(a) From above, we are given an initial point in the solution (y(to) = yo), and an equationthat describes the slope of the solution everywhere, Eq. 1. Use this information tofind the linear approximation to the solution at the initial point (to, yo).(b) Use the linear approximation to estimate the value of the solution at a nearby point,t₁ = to +h. We will denote your approximation by y₁. Provided that h is sufficientlysmall, the line tangent and the solution will be close, and y₁ will be a reasonableapproximation of the actual value of the solution, y(t₁).(c) Now, find the equation of the line that goes through the point (t₁, y₁) and has thesame slope the solution would have at that point, as prescribed by the differentialequation.(d) We may once again use this line to estimate the value of the solution at a nearbypoint. Consider t₂ = t₁+h. Estimate the value of the solution at the point t2, whichwe will denote by y/2.(e) Generalize: come up with an algorithm to compute yn, the estimated value of thesolution at the point tn = to + nh.(f) We can model the population y of bunnies in a park by the differential equationdydt= ky(N - y)(2)where k is the rate of growth of the population, N is the carrying capacity, and t ismeasured in months. Consider a population that grows at a rate k = 0.5 per month,and a carrying capacity N = 100 bunnies. If the initial population of bunnies is7, use the algorithm you constructed in part (e) to estimate the number of bunniesthat will be living in the park after a year. Try at least three different values of thestep-size h. Which one provides the most accurate estimate?(g) Find the exact solution for the bunny population as a function of time, y(t).

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Note- In this question part (a) and part (c) alredy solve by experts and good explain each part we…