Verify whether the general solution \(y=e^xcosx\) does satisfy the D.E. Y” -2Y’ + 2Y= 0
y = e^x cos (x)
y ' = e^x cos(x) - e^x sin(x)
y " = e^x cos (x) - e^x sin (x) - e^x sin (x) - e^x cos(x) = -2 e^x sin (x)
So
y" - 2y' + 2y =
-2 e^x sin (x) - 2 [ e^x cos(x) - e^x sin(x) ] + 2 [ e^x cos(x) ] = 0
