Find a formula involving integrals for a particular solution of the differential equation y 3y + 3y y = g(t). If g(t) = t 2et , determine Y(t).

Basic Math Sciences Notes Rules for Exponents; n m n+m b * b = b o Multiply the base but add the exponents 5 7 12 x * x = x m-n n-m 1/b = b o Dividing the same base but subtracting the exponents 5 7 2 y /y = 1/y (b ) = b m*h o Power raise to a power, multiply the exponents 5 2 10 (z ) = z (a * b) = a * b n n n n (a/b) = a /b Examples; (5x) = (5 ) (x ) = 625x 4 2 n n o (a *b) = a * b 14 8 3 8-(-2) 3 10 3 30 (-30a b ) (-3b ) (-3b ) -27b ―――― = ―――― = ――― = ――― (10a b ) -2