Question: Suppose that we use Euler's method to approximate the solution to the differential equationdydx=x5y;,y(0.5)=7Let f(x,y)=x5y.We let x0=0.5 and y0=7 and pick a step size h=0.2.
Suppose that we use Euler's method to approximate the solution to the differential equationdydx=x5y;,y(0.5)=7Let f(x,y)=x5y.We let x0=0.5 and y0=7 and pick a step size h=0.2. Euler's method is the the following algorithm.From xn and yn, our approximations to the solution of the differential equation at the nth stage, we findthe next stage by computingxn+1=xn+h,yn+1=yn+h*f(xn,yn).Complete the following table. Your answers should be accurate toat least seven decimal places.The exact solution can also be found using separation of variables. Itisy(x)=Thus the actual value of the function at the point x=1.5y(1.5)=
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