Question

Separable equations
\[\frac{dy}{dx}=\frac{ycosx}{1+y^{2}}\]
\[\int \frac{1+y^{2}}{y}dy= \int cosx dx\]
\[\int \frac{1+y^{2}}{y}dy= sinx +C\]

Answer 1

u=1+y^2 ?

Answer 2

simplify the integrand on the left side by doing long division first....

Answer 3

ok

Answer 4

y+ 1/y

Answer 5

\[\huge \frac{1+y^2}{y}=\frac{1}{y}+\frac{y^2}{y}=y^{-1}+y \]

Answer 6

yep... that's easily integrated huh?

Answer 7

yep y^2 /2

Answer 8

what about y^-1 ?

Answer 9

1+ y^2 /2

Answer 10

1+ (y^2)/2

Answer 11

wait...

Answer 12

\[\large \int \frac{1}{y}dy=lny+C \]

Answer 13

duh...thanks

Answer 14

lolz

Answer 15

yw...:)