Question

using variation of parameter: find the solution to;

y''+y=tan(x)

Answer 1

y=tan(x)

Answer 2

\[y=y_h+y_p\]
\[y=c_1cos(x)+c_2sin(x)+y_p\]
\[W_m=\begin{pmatrix}
cos(x)&0&sin(x)\\-sin(x)&tan(x)&cos(x)\end{pmatrix}\]

Answer 3

whoa amistre, why is your wronskian a determinant of a 2x3 matrix?

Answer 4

how can you even take that determinant?

Answer 5

lol, its just a setup that makes my life easier

the column 1 and 2 make up the "W"

and the W1, W2 is set in position for using the middle column

Answer 6

\[W=\det \left[\begin{matrix}\cos x & \sin x \\ -\sin x & \cos x\end{matrix}\right]=1\]I think you can take it from here, no?

Answer 7

he column 1 and 3 make up the "W"

Answer 8

YES, i EVEN HAVE IT THAT FAR ALREADY ;)

Answer 9

sorry, pinky hit a caps ...

Answer 10

ok, so we got\[y_p=-\cos x\int\sin x\tan xdx+\sin x\int\cos x\tan xdx\]and you are having trouble with the integrals, or what?

Answer 11

i was having troubles remembering how to set up for the integrals; I couldnt recall if it was your way there or if it was int wy .... that helped :)

Answer 12

variation of parameters just follows that formula
If there is another way top set it up I don't know
I'll let you take it from here ;)

Answer 13

i learned it the long way, so the formula itself is a bit vague to me....

Answer 14

http://integral-table.com/downloads/ODE-Summary.pdf
I use this when I forget the formula

Answer 15

i know it ends up like that as a result tho

Answer 16

ooooo!!! ... you gots a cheat sheet :)

Answer 17

all the good ODE stuff is on that page, in case you forget it
it's on my favorites list
(makes me look smarter than I am, jeje)

Answer 18

...but I derived it once upon a time, so I don't feel too guilty using it :)