Question

differential equations exact equations
(3x^2y-6x)dx+(x^3+2y)dy=0

Answer 1

Anything in particular about it troubling ya or do you wanna go through it all?

Answer 2

well i can show that they are exact but after that it gives me a lil trouble. Im going to try working through it again

Answer 3

last one that is giving me trouble for tomorrows test review

Answer 4

Alright, cool, we know theyre exact. So now we just take the terms grouped with dx and integrate with respect to x.

Answer 5

im at the part where we take derivative of f with respect to y and i get x^3y^2/2-3x^2y+g'(y)

first part where its x^3y^2/2 doesnt seem right to me

Answer 6

Okay, so lemme catch up to ya then. So we take the integral with respect to x and get:

\[x^{3}y -3x^{2} + g(y)\] Now we take the derivative with respect to y and set it equivalent to our original group of dy terms from the original problem. So if I do that I have:

\[x^{3} + g'(y) = x^{3} + 2y\]
\[g'(y) = 2y\]

Answer 7

oh my bad i took integral not differentiate -_-

Answer 8

always integrate with respect to the derivative part. If its dx, integrate to dx, if its dy, integrate to dy. and differentiate to the opposite one. If you got (------)dx, differentiate to y, if you got (------)dy, differentiate to x.

Answer 9

ok so g(y)=y^2

Answer 10

Right.

Answer 11

so final answer should be f=x^3y-3x^2+y^2 correct???

Answer 12

\[x^{3}y - 3x^{2}+y^{2} = C\]

Answer 13

That method is great, I like to do it like this personally though.

Integrating M with respect to x:\[\Large x^3y\color{royalblue}{-3x^2}+\color{orangered}{f(y)}\]
Integrating N with respect to y:\[\Large x^3y+\color{orangered}{y^2}+\color{royalblue}{g(x)}\]
And just match up the pieces from there :3
I always get tripped up doing that derivative step lol.

Answer 14

Still gotta set it to C, otherwise youre good :3 And yeah, I somehow picked up the pattern pretty fast on the exact. Im just glad I rememebr xD

Answer 15

cool thanks for the help guys....@zepdrix im gonna have to try the method you mentioned. calling it a night guys i appreciate the help....gotta get some rest for tomorrows test!

Answer 16

have a good night!!!!

Answer 17

Night and good luck :3

Answer 18

night \c: