Question

Dy/dx=xlny. Y(1)=1

Answer 1

Use seperation of variables first..

Answer 2

Dy/ln(y)=xDx

Answer 3

oh yeah...cross multiplied wrong srry

Answer 4

I got x^2/2+c but not sure of dy/lny

Answer 5

\[\int\limits_{a}^{b} \frac{ 1 }{ \ln(y) } = \int\limits_{a}^{b} x dx\]

Answer 6

\[\int\limits\limits_{}^{} \frac{ dy }{ \ln(y) } = \int\limits\limits_{}^{} x dx\]

Answer 7

Help with left side

Answer 8

I'm not really sure....

Answer 9

That should be ln[ln(y)]

Answer 10

Then raise both sides by "e" the natural number to remove the natural log.

Answer 11

And then again to solve for "y"

Answer 12

ahhh

Answer 13

is your anser in teh book: \[y=e^{ce^{x^{2}/2}}\]

Answer 14

I think they want a particular solution using the initial value

Answer 15

Then I am very wrong..

Answer 16

If what you wrote is correct then all you would have to do is change y to 1 and x to 1 then solve for c

Answer 17

If \[y=e^{ce^{x^{2}/2}}\] then solving for y(1)=1 you get\[1=e^{ce^{1/2}}\] and by taking the natural log of both sides you get: \[\ln(1) = ce^{1/2}\] and then \[0=ce^{1/2}\] with c=0. Then you can see that \[y=1\] as stated.