From a cubic function where y(0)=1, y(1)=0, and where there is a local max at y(5/13) I created a basic separable differential equation problem. I wanted to analyze how well different ordered Runge Kutta methods works in an interval [0,1]. Here it is: dy/dt=-6(6/13)1/3(y-343/468)2/3 , y(0)=1 This ODE yields the cubic solution of y=1/468(-12t+5)3+343/468 Now it is clear that y(1)=0 But using the several Runge Kutta programs with various computer software (mathematica, ti-nspire cas, mathstudio, etc.) yields a complex solutions for y(1). For example, using the classical RK4 with h=.1 yields y(1)=0.718779+.005811i. I don't see how the programs get a complex solution when all the functions have no even roots. Does anyone what is going on with these programs?