Predictor-Corrector and trapeze method

Predictor-Corrector method. Write a program that solves

y′ = f(x,y)

y(x0)= y0, using trapeze method with fixed step h. For the predictor use Euler's method. Solve next equation with the step size h=0.5 and 0.25 on [0,10]:

y′=-y+2*cos(x); y(0)=1; y(x)=sin(x)+cos(x).

Please help me solve this problem, i also have to do a GUI for it, but at least i want to know the code that just solves the equation.