Question

solve by linear DE:

\[(2xy + x^2 + x^4)dx - (1+x^2)dy = 0\]

Answer 1

i think this is solveable by exact DE easily...but my problem is if it can be solved by linear DE..if so how?

Answer 2

It is exact.
However it can also be solved by linear DE if you know how to solve for \(y' + p(x).y = q(x) \) (which indirectly uses the concept of exactness)

Answer 3

how can i put it in that form??

Answer 4

\((2xy+x^{2}+x^{4})dx = (1+x^{2})dy \)

\[\Large \Rightarrow \frac{dy}{dx} = \frac{2x}{1+x^{2}}y + x^{2}\]\[\Rightarrow \Large y' - \frac{2x}{1+x^{2}}y = x^{2}\] where \(\Large p(x) = \frac{-2x}{1+x^{2}}, q(x) = x^{2} \)

Answer 5

OHHHH I SEE IT NOW!!!! (although you forgot + x^4 there)

Answer 6

oh nevermind

Answer 7

i saw what you did

Answer 8

nice ..incredible