Find the general solution to y 7y 8y 0 Give your answer a

Find the general solution to y\'\' + 7y\' - 8y = 0. Give your answer as y =... . In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter c1 as c1 and c2 as c2.

Solution

y\'\' + 7y\' - 8y = 0
above equation can be reduced to:
D^2 + 7D - 8 = 0
D^2 + 8D - D - 8 = 0
(D + 8)(D - 1) = 0
D = 1, -8
Hence
y1 = C1e^x
y2 = C2e^-8x

Hence
y = y1 + y2
y = C1e^x + C2e^-8x