Please solve the following by hand Show work Solve the follo

Please solve the following by hand. Show work.

Solve the following problem over the interval from x=0 to 1 using a step size of 0.25 where y(0)=1 Display all your results on the same graph. Dy/dz=(1+4x)square root y Analytically. Using Euler\'s method. Using Heun\'s method without iteration. Using Ralston\'s method. Using the fourth-order RK method.