Need help with following three differential equations. Help is really appreciated!
First:
Solve the differential equation , y(0) = 1.
Second:
, y(0)=5.
Third:
that have the value 4 when x=0
Yes, that first equation is linear and so you can get an integrating factor this way. It is , not . After that you are good
until here. , not .
-->
-->
=
But mr fantastic told you the equation was separable. It is much easier to do so that . Integrating, so that .
Well, it is not hard to check yourself: if then while . So . No, that is not "3" and so your solution does not check.Which gives
Is this right?
No, the integral of 8 sin(x) is -8 cos(x).Second:
integrating factor =
One of the things you should have learned long ago is that .)
Thats about how far I can go, and don't know if its right.
Third:
Divide with on both rows and integrate both:
Thats how far I can go.
. Let u= y/3.