DSolve[Derivative[2][y][x] == -(a^2*n*Sec[a*x]^2*(Cos[a*x]^2 + (-1 + n)*Sin[a*x]^2)*y[x]) - a*(-1 + n)*Sec[a*x]^2*Sin[2*a*x]*Derivative[1][y][x],y[x],x]