Question

Find the general solution of xy'+(ln x)y=0.

Answer 1

@ganeshie8

Answer 2

looks separable ?

Answer 3

But how do I do this?

Answer 4

\[\large \begin{align} \\
xy'+(\ln x)y &=0 \\\; \\
x\frac{dy}{dx} &=-(\ln x)y \\\; \\
\frac{dy}{y} &=-\frac{\ln x}{x} dx \\ \; \\
\int \frac{dy}{y} &=-\int \frac{\ln x}{x} dx \\ \; \\

\end{align}\]

Answer 5

Let me try. Please don't leave.

Answer 6

integrate ^^

Answer 7

ok good luck !

Answer 8

How do I integrate ln(x)/x?

Answer 9

yes! don't forget negative sign haha

Answer 10

Do by part haha

Answer 11

u susbtitution may work :)
u = ln(x)

Answer 12

actually u is easy

Answer 13

try and see!

Answer 14

Yes, I got the right answer. Thank you, ganeshie8.

Answer 15

Good!

Answer 16

yw :)