The explicit one-dimensional Runge-Kutta 4-th order method, description, numerical implementation. Examples integration:

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The explicit one-dimensional Runge-Kutta 4-th order
method, description, numerical implementation. Examples
integration:
a) dx/dt=t on segment [0,1], x(0)=0;
b) dx/dt=t2 on segment [0,1], x(0)=0;
c) dx/dt=t3 on segment [0,1], x(0)=0;
d) dx/dt=sin(t) on the segment [0,π], x(0)=0;
e) dx/dt=cos(t) on the segment [0, π], x(0)=0;
f) dx/dt=et on the interval [0,1], x(0)=1;
g) dx/dt=1/t on the interval [1,e], x(1)=0.
Calculation of the error at the right end of the interval (the
exact analytic solution minus what the program calculated) for
different integration steps h. And also realize the code in c/c++
programming.