Math Fun

[JamesKane]

Solve the following differential equations and receive a prize;

Find the equation Z(x,y) given the differential equation
dZ(x,y) = [y^2+Cos(x)]dx + [2xy + Sin(y)]dy = 0

hint: Use Partial derivatives

From here

Solution

px will be used as partial derivative
dx will be used as derivative

[y^2+Cos(x)]dx + [2xy + Sin(y)]dy is in the form pZ/px * dx + pZ/py * dy = 0

Step 1] Lets see if this is an exact differential, so let us define two variables
pZ/px = m = y^2 + Cos(x)
pZ/py = n = 2xy + Sin(y)

Now if they are exact differentials then taking pM/py should equal pN/px

pM/pY = p/py(y^2) + p/py(Cos(x)) = 2y + 0
pN/pX = p/px(2xy) + p/px(Sin(y)) = 2y + 0

We have a winner, they are the same, so we can use the exact differential method to solve.

2] Lets integrate to find our function z with partial derivative with respect to x

Let z = integral of m * dx = integral of y^2 + cos(x) dx = xy^2 + sin(x) + H(y) = C1

3] H(y) is the left over junk from partial derivatives, so lets get rid of this

Lets use a partial derivative of xy^2 + sin(x) + H(y) with respect to y and set it equal to pZ/py(n) to find the derivative of H(y).

pZ/py = n = 2xy + Sin(y) = 2yx + H(y) = 0 so H(y) = sin( y )

integrate both sides with respect to dy to find H(y) = -cos(y) + C2

4] Lets insert H(y) back into the function and let C3 = C1 + C2

z = xy^2 + sin(x) - cos(y) = C3

[Ramirezoid]

once more, with feeling.

[Coolm4n]

Bah, I don’t like maths. :sick:

[Someonerandm]

No clue whatsoever.

[JamesKane]

We have a winner
https://forums.blackmesasource.com/showpost.php?p=55376&postcount=2294

I edited the above post to show the solution…

[blue]

thank you, i dont do meth.

[Someonerandm]

So, where are our developments?

[mattemuse]

I agree, developments pleex

[JamesKane]

@Someonerandm

So, where are our developments?

Getting developed of course

[Rossman]

Thanks James… fuck[/SIZE]

[Sky_Monster]

Sigh… I’m doing this sort of shit at school atm…

Edited for your interpretation…

[mattemuse]

@Sky Monster

Sigh… I’m doing this sort of shit at school atm…

differential equations? no you aren’t.

[Sky_Monster]

@mattemuse

differential equations? no you aren’t.

What country are you in?

[Keresh]

Are you talking about primary school or high school?

[Sky_Monster]

Unless Mattemuse goes to an Australian Independent (Private) High school I doubt he can really argue me on this…

[Collision]

Yes, we do shit like that in Australian High school.

We have elective Math Class’s in Grade 11 and 12 that are like, super advanced shit.

[Grey_Acumen]

damn, I haven’t done this crap in a long time. i should go back over my calculus book and brush up on all of this. Should probably go over my physics textbook too.

Now if you want to try solving a REALLY difficult problem, try figuring out what real life applications this particular problem has, and explaining the circumstances under which you will be able to find the initial values for all parts of the equation that you need to solve, but not be able to find the values for the answer without solving the equation.

[Keresh]

Haha, super advanced… We also had that in high school so it’s nothing extraordinary.

[The_Assassin47]

@Collision

Yes, we do shit like that in Australian High school.

We have elective Math Class’s in Grade 11 and 12 that are like, super advanced shit.

I did Multivar Dif EQ senior year. With seven of my peers. In a 47 senior class size. (We were a smart class)
Its possible he did.

[zim]

@Collision

Yes, we do shit like that in Australian High school.

We have elective Math Class’s in Grade 11 and 12 that are like, super advanced shit.

General maths FTW.