Question: how to solve non-linear equation?

restart;
with(PDETools);
diff(r(t), t)-(diff(a[3](t), t))*r(t)/a[3](t)+a[1](t)*p[3](t)-3*r(t)*r(t) = 0;
                                        
dsolve(diff(r(t), t)-(diff(a[3](t), t))*r(t)/a[3](t)+a[1](t)*p[3](t)-3*r(t)^2 = 0, r(t));

 it does not give any solution ,please help.
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