Question

y''-10y'+25y=0 y(0)=2 y'(0)=-1

Answer 1

y''-10y'+25y=0

first find the auxiliary equation
by setting y'=m, y''=m^2

Answer 2

ok, I did --> c1e^5x + c2e^5x

Answer 3

But now I don't know what I need to make now :(

Answer 4

in the case of repeated roots m=5,5, it's

\[y=(c_1+c_2x)e^{5x}\]

Answer 5

hummm OK, and after it ?

Answer 6

ok so now you have the general form ,

\[y(x)=(c_1+c_2x)e^{5x}\]

use the initial values to find the constants

\[y(0)=(c_1+c_2(0))e^{5(0)}=2\]


simplify to find c_1

Answer 7

...

Answer 8

Ok,