solving ODE using numerical methods

program to solve ODE using different numerical methods

A most general form of an ordinary differential equation (ode) is given by f( x, y, y', . . ., y(m) ) = 0
where x is the independent variable and y is a function of x. y', y'' . . . y(m) are respectively, first, second and mth derivatives of y with respect to x. ref: https://mat.iitm.ac.in/home/sryedida/public_html/caimna/ode/intro.html
example :
program to solve 1st Order differential Equation using different numerical methods
comparing the results with ODE45 and to find max error for a user defined step size " h "
enter the function in form of @(x,y): @(x,y)cos(x)-log(y)
enter initial "x" value : 1
enter final "x" value : 3
enter initial "y" value : 1
enter "h" value : 0.1
maximum error ode45 vs Euler= 0.030403 with step size h= 0.1
maximum error ode45 vs RK-4= 1.3012e-06 with step size h= 0.1
maximum error ode45 vs Heuns(Rk-2)= 0.00095811 with step size h= 0.1
maximum error ode45 vs Midpoint= 0.0009912 with step size h= 0.1
maximum error ode45 vs Backward Eulers= 0.044459 with step size h= 0.1