Question: Trouble obtaining numerical solutions to series of second order differential equations using dsolve

I want to solve a series of differential equations, and then plot the results, but I'm having a bit of trouble with evaluating them using dsolve. My code is:

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restart;

c:=1;
mu:=0.3;
m1:=1-mu;
m2:=mu;
x1:=mu;
x2:=mu-1;
omega1:=1/2(mu(1-mu)-3);
omega:=1+omega1/c^2;
r1:=sqrt((x(t)-x1)^2+y(t)^2);
r2:=sqrt((x(t)-x2)^2+y(t)^2);
A:=diff(y(t),t)*x(t)-diff(x(t),t)*y(t);
rsquared:=x(t)^2+y(t)^2;
usquared:=diff(x(t),t)^2+diff(y(t),t)^2;

EOM:=

diff(x(t),[x$2])=2*diff(y(t),t)+x(t)-m1(x(t)-x1)/r1^3-m2(x(t)-x2)/r2^3+1/c^2(6(m1/r1+m2/r2)(diff(y(t),t)+x(t)/2)+2*omega1(diff(y(t),t)+x(t))+m1*m2((x(t)-x1)/r1^3+(x(t)-x2)/r2^3)+(4*diff(y(t),t)+7*x(t)/2)((m1(x(t)-x1)*x1)/r1^3+(m2(x(t)-x2)*x2)/r2^3)+(m1(x(t)-x1)/r1^3+m2(x(t)-x2)/r2^3)(m1/r1+m2/r2-3(2*A+rsquared+usquared)/2+3*diff(x(t),t)(diff(x(t),t)-y(t)))-3(2*diff(y(t),t)+x(t))(m1/r1+m2/r2)-(m1(x(t)-x1)/r1^3+m2(x(t)-x2)/r2^3)(-3(m1/r1+m2/r2)-(2*A+rsquared+usquared)/2-(diff(x(t),t)-y(t))^2)+3(m1/r1^3+m2/r2^3)*diff(y(t),t)*(diff(x(t),t)-y(t))*y(t)-7/2*(m1*x1/r1+m2*x2/r2)-3/2(m1(x(t)-x1)(x1)^2/r1^3+m2(x(t)-x2)(x2)^2/r2^3)+3/2*y(t)^2(m1(x(t)-x1)(x1)^2/r1^5+m2(x(t)-x2)(x2)^2/r2^5)-y(t)(diff(y(t),t)+x(t))(-diff(x(t),t)+y(t))(m1/r1^3+m2/r2^3)),

diff(y(t),[t$2])=-2*diff(x(t),t)+y(t)-y(t)(m1/r1^3+m2/r2^3)+1/c^2*((m1*x1/r1^3)(-3*diff(x(t),t)*diff(y(t),t)-7*x(t)(diff(x(t),t)-y(t)/2))+(m1*x1^2/r1^3+m2*x2^2/r2^3)(4*diff(x(t),t)-5*y(t)/2)+m1*m2*y(t)(1/r1^3+1/r2^3)+3/2*y(t)^3(m1*x1^2/r1^5+m2*x2^2/r2^5)+2*omega1(-diff(x(t),t)+y(t))-(diff(y(t),t)+x(t))(-diff(x(t),t)+y(t))(m1(x(t)-x1)/r1^3+m2(x(t)-x2)/r2^3)+(m1/r1^3+m2/r2^3)(y(t)(-2*A-rsquared+4(m1/r1+m2/r2)-usquared+(diff(y(t),t)+x(t))^2)+3(diff(y(t),t)+x(t))(diff(x(t),t)*x(t)+diff(y(t),t)*y(t))));

INIT:=x(0)=2,y(0)=2,D(x)(0)=0,D(y)(0)=-1;

#initial conditions are arbitrary

dsolve([EOM,INIT],numeric,{x(t),y(t)});

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It gives me the error message:

Error, (in dsolve/numeric/process_input) input system must be an ODE system, got independent variables {t, 1/((x(t)-.3)^2+y(t)^2)^(3/2)+1/((x(t)+.7)^2+y(t)^2)^(3/2), .7/((x(t)-.3)^2+y(t)^2)^(3/2)+.3/((x(t)+.7)^2+y(t)^2)^(3/2), -3*(diff(x(t), t))*(diff(y(t), t))-7*(x(t))(diff(x(t), t)-(1/2)*y(t)), diff(x(t), t)-(1/2)*y(t), 4*(diff(x(t), t))-(5/2)*y(t), (y(t))(-2*(diff(y(t), t))*x(t)+2*(diff(x(t), t))*y(t)-x(t)^2-y(t)^2+4-(diff(x(t), t))^2-(diff(y(t), t))^2+(diff(y(t), t)+x(t))^2)+3, -2*(diff(y(t), t))*x(t)+2*(diff(x(t), t))*y(t)-x(t)^2-y(t)^2+4-(diff(x(t), t))^2-(diff(y(t), t))^2+(diff(y(t), t)+x(t))^2}