Problem 1 35 pts Consider the differential equation dydx

%% Problem #1 - 35 pts % Consider the differential equation % dydx = (1+4*x)*sqrt(y) Not necessarily MATLAB code

% x = 0 to 1

% y(0) = 2 %

a) 10pts Solve the equation analytically using MATLAB\'s symbolic capability % (Note... this is a function of both x and y, not t and y. Make the % appropriate adjustments...) % ***************************Note************************** % You will get two solutions - only consider the first when you create a % plot in part d % ************************************************************ %%

b) 10pts Solve the equation using Heun\'s method, with a step size of 0.1. % Do not create a separate function, just create the code right in this % file

%%c) 10pts Solve using the built in ode solver. Present your results as a table % of x and y values.

%% d) Plot all three solutions on the same graph. The analytical solution should % be a solid red line, the numerical solution using Heun\'s rule should be represented % with a series of green circles and a green line, and the solution from the built-in MATLAB function % Should be blue circles and a blue line. Add a legend... and Don\'t forget a title, % and axis labels.

Solution

the answer is in the attached file