2. We want to solve the differential equation y" -6 y" + 11 y'-6y=0.

i. Find the general solution by finding the roots of the appropriate polynomial. (If you do this

correctly the roots are simple integers.)

ii. Find the solution to the d.e. with y(0) =3, y'(0) = 6 and y" (0) = 14.

iii. With the initial conditions as in part ii solve the d.e. by power series. This means that you

have to figure out the general pattern for the coefficients and then identify the resulting function.

iv. Suppose k(x) = 1+x+x²-x+x5 + higher powers unknown to us. We wish to find the power

series 1(x) for which k(x) 1(x) = 1. Find the series for I through the fourth power of x:

1(x) = A+ Bx+C x² +Dx³ +Ex+...,

where A, B, C, D and E are numbers to be determined,