Question

The solution of
(x+logy)dy+ydx=0 when y(0)=1 is?

Answer 1

Looks like an exact equation.

Answer 2

Attempt:
\[\LARGE (x+\log y)\frac{dy}{dx}=-y\]
\[\LARGE \frac{dx}{dy}=-\frac{(x+logy)}{y}\]
\[\LARGE \frac{dx}{x+\log y}=- \frac{dy}{y}\]
urg doesnt work :/
variable seperable fails..
nor its homogenous..
not sure about linear..

Answer 3

It's an exact equation.

Answer 4

There is an \(f(x,y)\) such that:\[
f_xdx+f_ydy=0
\]

Answer 5

wait let me try now then

Answer 6

thanks for the clue

Answer 7

why not ask the question in here?

Answer 8

xy is there for sure..

Answer 9

\[
[x\ln(x)]'=\ln(x)+1
\]

Answer 10

\[
[x\ln(x)-x]'=\ln(x)+1-1=\ln(x)
\]

Answer 11

\[\LARGE xy+(y \log y-y)\]
seems so

Answer 12

\[+C\]

Answer 13

yup

Answer 14

\[
xy+(y\ln(y)-y)+C=C_2
\]

Answer 15

C=0 anyway,got the answer! thanks!