Consider the differential equation
(dx)/(dt)=7t^(2)-4(x)/(t),1<=t<=6
with the initial contition
x(0)=2.
(a) Solve the equation, analytically.
(b) Use the Taylor-series method to solve the equation, given the stepsize h=0.10000. Limit your results to five steps, with five significant figures. Limit the expansion to three terms.
(c) Use the simple Euler method to solve the equation, given the stepsize h=0.10000. Limit your results to five steps, with five significant figures.
(d) Use the modified Euler method to solve the equation, given the stepsize h=0.10000. Limit your results to five steps, with five significant figures