I've been attempting these two questions a few times and I countinue to get them wrong.

1) Find y as a function of x if

y(1)=6, y'(1)=-5

So I solved the Homogenous equation as a Euler equation. My homogeneous solution is yh= C1x^(8)+C2ln(x)x^(8)

then i proceeded with undetermined coefficients and ended up with 151/25x^8-1336/25ln((x))x^8+x^(3)/25

Whats wrong with the method?

2) Use the method of undetermined coefficients or the method of differential operators to find one solution of

y'' -8y' + 43y = 32e^4t(cos(5t))+64e^4t(sin(5t))+ 7e^0t

(It doesn't matter which specific solution you find for this problem.)

My guess for yp was Ae^4t cos(5t)+Be^ 4t sin(5t)

And I used the undetermined coefficent method to find A=16 and B=32.

Thanks.