Hi. I need some help with some questions that we are required to do as coursework. I've tried very hard to find the methods for these but unfortunately many of them aren't clear to me, I'm at a dead end and I hope I can get some help here. I'd appreciate it much. I know the sticky says to post any workings I have attempted but honestly I'm at a complete loss here, I'm embarrassed to admit 
The problems involve Euler method, Modified Euler method and finding the general solution of an ordinary differential equation.
I will post the questions here but I don't want just the solutions... it would help me a lot if you could perhaps talk me through the workings out. Thanks!
Q1) Solve the equation (dv/dt)=t+(v/t), subject to v(1) = 1, to find v(2) working to 5 significant figure accuracy throughout and using:
(a) Euler’s Method with step lengths h = 0.5, and h=0.25.
(b) The Modified Euler Method with step lengths h = 0.5 and h = 0.25.
(c) Given that the actual value of v(2) is 4m/s^2 calculate the absolute values of the errors in your results for parts (a) and (b). What happens to the size of the error for Euler’s Method when the value of h is halved? What happens to the size of the error for the Modified Euler Method when the value of h is halved?
(Please note that for these methods there is no difference between dv/dt=f(t,v) and dy/dx=f(x,y) .)
Q2) Find the general solution of the ordinary differential equation (dy/dx)+xy=x
and find the solution, y(x), that satisfies y(0)=-1.
Q3) Find the general solution of the ordinary differential equation (d^2y/dx^2)+4y=cos2x
The problems involve Euler method, Modified Euler method and finding the general solution of an ordinary differential equation.
I will post the questions here but I don't want just the solutions... it would help me a lot if you could perhaps talk me through the workings out. Thanks!
Q1) Solve the equation (dv/dt)=t+(v/t), subject to v(1) = 1, to find v(2) working to 5 significant figure accuracy throughout and using:
(a) Euler’s Method with step lengths h = 0.5, and h=0.25.
(b) The Modified Euler Method with step lengths h = 0.5 and h = 0.25.
(c) Given that the actual value of v(2) is 4m/s^2 calculate the absolute values of the errors in your results for parts (a) and (b). What happens to the size of the error for Euler’s Method when the value of h is halved? What happens to the size of the error for the Modified Euler Method when the value of h is halved?
(Please note that for these methods there is no difference between dv/dt=f(t,v) and dy/dx=f(x,y) .)
Q2) Find the general solution of the ordinary differential equation (dy/dx)+xy=x
and find the solution, y(x), that satisfies y(0)=-1.
Q3) Find the general solution of the ordinary differential equation (d^2y/dx^2)+4y=cos2x
