Question

Solve DE by reduction to constant coefficients

Answer 1

\[x^2y''-3xy'+13y=4+3x\]

Answer 2

i did quadratic and used reductio nto find the y_c which is correct

Answer 3

\[y_c=x^2(c_1cos(3ln(x)+c_2sin(3ln(x))\]

Answer 4

\[y_p=Ax+B\]
\[y_p'=A\]
\[y_p''=0\]

Answer 5

switch the x with t

Answer 6

\[y''-4y'+13y=4+3t\]
\[0-4A+13At+13B=4+3t\]

Answer 7

\[0-4A+13Ax+13B=4+3x\]
\[0-4a+13Ae^t+13B=4+3e^t\]

Answer 8

is ther aything wrong with this?

Answer 9

because this was exactly what i did and i still come out with the wrong answer

Answer 10

@amistre64

Answer 11

I can't figure out why these answers are coming out wrong?

Answer 12

2 months of summer vacation, id have to read up on this to refresh

Answer 13

the complementary is correct but idk how to do the nonhomogeneous. my book simply says use the new equation and solve using the procedures from a few sections however that doesn't work

Answer 14

wronskian works if youve got the homogenous part

Answer 15

yes but idk if thta's what it wants me to do

Answer 16

it says sub x=e^t to get it with constant coefficients

Answer 17

i do that

Answer 18

and i get my complementary.. Since it's in constant coefficients ican use superposition

Answer 19

with \[y_p=Ax+B\]

Answer 20

however when i do this i get a completely different answer than the book and i have no idea how they got it

Answer 21

this looks like its pretty basic, but id have to read thru it a few more times to be sure.

http://books.google.com/books?id=BnArjLNjXuYC&pg=PA167&lpg=PA167&dq=reduction+to+constant+coefficients&source=bl&ots=_dUSk8oQTn&sig=SEKZV10njSqZAyfNbrBqm0HrgOk&hl=en&sa=X&ei=UIz8T82QN4e88ASeod3bBg&ved=0CEwQ6AEwAQ#v=onepage&q=reduction%20to%20constant%20coefficients&f=false

Answer 22

that is my book-.-

Answer 23

:)

Answer 24

ok, so are you sire youre Yc is good?