Question

show that the given diffrential equation is homogeneous...

Answer 1

which kind of homogenous do you mean

Answer 2

substitute tx for x and ty for y, and then compare the resulting equation with the original equation

Answer 3

if u get same diff. eq again, then its homogeneous

Answer 4

homogeneous equation is
log(x) = cos(y/x) - 1

Answer 5

solution:
http://screencast.com/t/DN7q13Zxty

Answer 6

@ash2326
help me out with this one if you can

Answer 7

Just a moment

Answer 8

thanks @integralsabiti

Answer 9

We have
\[\frac{dy}{dx}-\frac {y}{x}+cosec {\frac y x}=0\]
Put
\[\frac{y}{x}=t\]
\[y=xt\]
\[\frac {dy}{dx}=t+x\frac{dt}{dx}\]
Do you get this part?

Answer 10

yah.. now can you tell me how to find its solution?

Answer 11

Let's plugin this in the original DE
\[\frac{dy}{dx}=t+x\frac{dt}{dx}\]
\[t+x\frac{dt}{dx}-t+cosec \ t=0\]
\[x\frac{dt}{dx}+cosec\ t=0\]
do you get this

Answer 12

@shruti ???

Answer 13

yes..now next what i have to do?

Answer 14

It's easy
\[x\frac{dt}{dx}+cosec\ t=0\]
\[x\frac{dt}{dx}=-cosec\ t\]
\[-\frac{dt}{cosec t}=\frac{dx}{x}\]
Now we have to integrate both sides
\[\int - \sin t dt=\int \frac{dx}{x}\]
Can you do this?

Answer 15

during intergrating process do i need to put those formulas only?
or something else?