how can i solve a differential system of non linear differential equations?

Hi, there is someone who can help me to solve this system of nonlinear differential equations with Newton Raphson method and thank you:

dx(1)=x(2); dx(2)=f*cos(lamda*t)-omega1^2*x(1)+M*alpha1*x(3)-alpha2*x(1)^3-mu1*x(2)+M*mu2*x(4)-mu3*x(2)^3; dx(3)=x(4); dx(4)=mu2*(x(4)-x(2))+alpha1*x(1)-omega2^2.2*x(3)