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1st check to make sure that they are exact.

\[\frac{ ∂M }{ ∂x }=\frac{ ∂N }{ ∂y }\]

check your partial derivatives. they should match up

either that or your teacher is horrible and wants you to solve this another way ll

integrating factor!

But I couldn't find a suitable integrating factor... :'(

ah yes this is not an exact solution one

UnkleR is right. Find the integrating factor to make it exact.

That's why I tried that partial.. - partial.. / ... to find one..

is that a hint... try getting one in such that it looks like above

You were on the right path.

\[\frac{ M_y-N_x }{ -M }\]

That's your integrating factor.

How... does... that... work...?

which bit

so you know
\[R,M,N\]substitute these in

take the partial derivatives

Is R the integrating factor?

yes

So, I should multiply the equation by R, right?

hmm, i cannot see any error in your working , how do you know its not right?

Because the book whispered me the answer :(

\[\tiny \text{can you whisper it to me too please , }\]

\[\tiny \color{white}{\mu =xy} \]

i see

\(\huge \color{red}{\mu =xy}\)
now, i see also.

\[21\sim16\]

I.... don't .... understand.... :(

\[R=\mu\]

Hmm... I should do it all over again?!

xy vs x^2 y^(5/2)
They look too different to me!

life would be so much easier if we could use substitution...and not IF.

Then, this, again, proves that life is not easy :(

well i used 6 bits of paper , and got the same answer we had before,
bother

6... bits?! of paper?!
:(

\(LS=(2m+4)x^ny^{m+1}-(6m+6)x^{n+1}y^m\)

checking RS

2m+4 = 3n+3
6m+6 = 4n+8
m=1
n=1

just one silly mistale!

*mistake

oh

i see it now , such a tiny tiny mistale

thank you so much @UnkleRhaukus , i learned a new method today...R=x^m y^n

OK, so now we have the integrating factor
\[R(x,y)=\mu(x,y)=xy\],
lets integrate!

\[c_1=-c\]

woo!

wasn't that fun?

Mummy!!!! I want to die :'(

lol :P

plz don't die.

She! It's a she!

Thanks for rescue!!!! I'm sorry for my silly mistake!!

*mistale

if you were wondering what the solution 'looks' like ,...

solutions*

Ugly :(
How do you get the plot?

i used a graphing program ,

That is..?