- #1
badman
- 57
- 0
hello everyone, i need some huge help here. here's the equation :
y''+y'-6y=10e^2x-18e^3x-6x-11.
complementary solution:c1e^2x+c2e^-3x
s1={e^2x}
s2={e^3x}
s3=(x,1}
ok since e^2x exists in the complimentary solution, it is therefore a solution, so i multiply it by x to get s'1{xe^2x}, so now i have that and my s2 and s3.
so i end up with this:
yp=Axe^2x+Be^3x+Cx+D
heres where i get confused do i use the product rule for Axe^2x, if so do i end up with these two derivatives: y'p=Axe^2x+2Ae^2x+...etc, y''p=Axe^2x+4Ae^2x+...etc. i really get confused with this product rule thing.
y''+y'-6y=10e^2x-18e^3x-6x-11.
complementary solution:c1e^2x+c2e^-3x
s1={e^2x}
s2={e^3x}
s3=(x,1}
ok since e^2x exists in the complimentary solution, it is therefore a solution, so i multiply it by x to get s'1{xe^2x}, so now i have that and my s2 and s3.
so i end up with this:
yp=Axe^2x+Be^3x+Cx+D
heres where i get confused do i use the product rule for Axe^2x, if so do i end up with these two derivatives: y'p=Axe^2x+2Ae^2x+...etc, y''p=Axe^2x+4Ae^2x+...etc. i really get confused with this product rule thing.