Question

PLEASE HELP!!!!


Let u = <7, -3>, v = <-9, 5>. Find 4u - 3v.

Answer 1

heres an example

Answer 2

(4y+2x-5)dx+(6y+4x-1)dy=0, y(-1)=2 i tried solving by seperation of variables but i didnt get newhere with that

Answer 3

You can do a linear transformation of the variables to get rid of the "-5" and "-1".

If
4y + 2x - 5 = 0
and
6y + 4x - 1 = 0
then
y = 9/2, x = -13/2

So let
x = u - 13/2
y = v + 9/2
du = dx
dv = dy

(4v + 2u) du = (6v + 4u) dv

dv/du = (2v + u)/(3v + 2u)

That is a homogeneous equation so substitute
v = wu
dv/du = w + u dw/du

w + u dw/du = (2w + 1)/(3w + 2)

Now you can separate the variables and integrate.

EDIT:

Duh!!!!! <face-palm>
I just saw your other question
You don't need to do all that stuff, it's an exact equation!!!

Integral is
4xy + x^2 - 5x + 3y^2 - y = c

y(-1) = 2
-8 + 1 + 5 + 12 - 2 = c
c = 8

Answer 4

honestly none of this makes sense to me @Jacob902