Let y(x) be the solution of the following initial-value problem. dxdy+3x2y=3x2,y(0)=7 (a) Use Euler's method and technology to compute y(1) with each of the following step sizes. (1) h=1 y(1)= (ii) h=0.1 y(1)= (iii) h=0.01y(1)= (iv) h=0.001y(1)= (b) Verify that y=1+6ex3 is the exact solution to the differential equation. We have y=1+6ex3y= We substitute the values of y and y and test the solution to see if the left hand side is equal to the right hand side. y+3x2y=+3x2(1+6ex3)=18x2ex3+=3x2 (c) Find the errors in using Euler's method to compute y(1) with the step sizes in part (a), (Round your answers to four decimal places.) h=1h=0.1h=0.01h=0.001error=lexactvalueapproximatevalue=error=lexactvalueapproximatevaluel=error=lexactvalueapproximatevaluel=error=lexactvalueapproximatevaluel= What happens to the error when the step size is divided by 107 When the step size is divided by 10 , the error estimate is (opproximately)