/sci/ - Science & Math

halp, I'm just a girl

As long as the solution contains the algebraic letters in both brackets then the solution is correct

>>4790677

solve for y in the solution, then plug back in the original

this is an exact diff eq I believe.

>>4790685
>>4790685
Prove it!

TITS OF GTFO!

>>4790695

lol no tits in sci

>>4790693

you want me to solve for Y and then substitute it in e^xy?
that'll make it even worse

>>4790687

hhmm I need to prove it though

take the total differential of it

>>4790700

To verify the solution yes...

or you could just solve it for yourself, it looks like an exact diff eq


(1+xe^(xy)) dy + (1+ye^(xy))dx=0
let M(x,y)=(1+xe^(xy)) and N(x,y)= (1+xe^(xy))

if dM/dx = dN/dy, then the diff eq is exact (take partial derivative)

then the solution is f(x,y) = integral of
(1+xe^(xy)) dy = integral of (1+ye^(xy))dx

>>4790704
TITS OF GTFO!

>>4790717

ok I'll just the the fucking thing
(1+xe^(xy)) dy + (1+ye^(xy))dx=0
let M(x,y)=(1+xe^(xy)) and N(x,y)= (1+ye^(xy))

if dM/dx = dN/dy, then the diff eq is exact (take partial derivative)

dM/dx = e^(xy) + xye^(xy) and dN/dy = e^(xy) + xye^(xy)

ok so the diff eq is exact

the solution is then
f(x,y) = integral of
(1+xe^(xy)) dy = integral of (1+ye^(xy))dx = C

f(x,y) = y + e^(xy) + h(x) = x + e^(xy) + k(y)
here h(x)=x and k(y)=y

hence the solution is

f(x,y) = y + x + e^(xy) = C

>>4790734

yay! thanks <3