Obtain the differential equation from  the equation y = e^x (a cos 2x + b sin 2x). where a and b are arbitrary constants.    

The given equation is
                      y = e^x (a cos 2x + b sin 2x)     ... (1)
Differentiating both sides w.r.t x, we get,
                         
    ...(2)
                                                                                  
Again differentiating w.r.t x,
       

or          

or          

or          
which is required differential equation.