Question

solve differential equation using exact method.
(x+y)^2dx+(2xy+x^2-3)dy=0 for the intial condition of y(1)=1

Answer 1

my answer was xy^2+x^2y-3y+x^3/3

Answer 2

=C

Answer 3

am i right ?

Answer 4

not sure how to apply initial condition

Answer 5

Ummm yah those are the same terms I'm coming up with!
\[\Large\int\limits (x+y)^2dx+\int\limits (2xy+x^2-3)dy=\int\limits 0\]Integrating each side gives us,\[\Large\sf \frac{1}{3}x^3+xy^2+x^2y-3y=c\]y(1)=1,
you can interpret this as, x=1 when y=1.
So just plug in a bunch of 1's to solve for c,\[\Large\sf \frac{1}{3}+1+1-3=c\]

Answer 6

i dont know what am smoking ....that so passed my mind

Answer 7

dont do DFQ for 2 days n i forget everything

Answer 8

heh XD

Answer 9

thx u