I have the two coupled ode’s as follows: $ $ \frac{\partial \bar{P}}{\partial t}=-0.5(mVa^3M^2exp{(-\sigma^2)}Sin{(2\phi(t)M)})$ $ , $ $ \frac{\partial\phi(t)}{\partial t}=\frac{\bar{P(t)}}{a^3V}$ $ . Where we take (a,V)=1, (m,M)=0.5 (I can vary them) and the initial conditions should be any, $ \bar{P_o}=0$ and $ \phi_o=0$ . Also, take $ \sigma=2 \,\,or\,\, 3$ . Again, I can vary the initial conditions. I have to solve this system numerically and plot results, and I have tried it by myself by taking guidance from the internet. Here is my try: NDSolve[{[x]'[t] == y[t]/(a^3 V), [y]'[t] == -0.5` a^3 E^(-(1/(M^2 rho^2)))m^2 M V Sin[2 M x[t]], x[1] == 1, y[1] == 1}, {x, y}, {t, 0, 100}] Plot[Evaluate[{{x[t], y[t]} /. %}], {t, 0, 100}, PlotRange -> All, PlotPoints -> 200]