In: Advanced Math
a) Check e^5x, xe^5x for independence using Wronskian
b) solve y" + 5y' + 6y = 0
c) convert the above equation to a system and solve it
d) Solve x^2y''-2xy'-4y= 0 by assuming solution of the form y=x^r
e) Solve the IVP using undetermined coefficients
y" -2y' -3y = 6
y(0)= 3
y'(0)=11