The exact solution can also be found for the linear equation. Write the answer as a function of x. y(a) = Thus the actual value of the function at the point x = 1.3 is y(1.3) =].Suppose that WE USE the Improved tuier's method to apprOXImate the SOlUtIOf'I t0 the CllTlE'l'Ehtlal equation dy _ : 1_ ' _ = 2_ d1: x 51;, y(0 3) Let an, y) = a: 1.51;. We let x0 = 0.3 and ya = 2 and pick a step size h = 0.25. The improved Euler method is the the following algorithm. From (mm 3;\"), our approximation to the solution of the differential equation at the nth stage, we find the next stage by computing the mstep x\" i 1 = $11 + h, and then In, the slope at (mm 3;\"). The predicted new value of the solution is 95ml : 19,; -l h - k1. Then we find the slope at the predicted new point k2 = f($n+1,zn+1) and get the corrected point by averaging slopes h yn+1: yin + 5061 + k2)- Complete the following table: 1'1 $7: yr: ll$11 Zn+1 ll$12 0 0.3 2 2.71.325 1.43"r'5 1Viiii; i:l i i 2i ii i i_i i . u. \\,_\\ Li i i 3i i i i_,i i i i i 4i