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
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Need help with following three differential equations. Help is really appreciated!
First:
Solve the differential equation
Second:
Third:
The first and third are seperable. The second uses the integrating factor.Quote:
Originally Posted by Anteeks
Need help with following three differential equations. Help is really appreciated!
First:
Solve the differential equation, y(0) = 1.
Second:
Third:
If you need more help, please show all your work and say where you're stuck.
Thank you!
First equation:
))
 )
-->
))
-->
=
)dy)
 )
=6)
Which gives
Is this right?
Second:
integrating factor =
)
 *)
)
^4)
}* )
Thats about how far I can go, and don't know if its right.
Third:
Divide withon both rows and integrate both:
 = x^5 )
Thats how far I can go.
Yes, that first equation is linear and so you can get an integrating factor this way. It isQuote:
Originally Posted by AnteeksThank you!
First equation:
, not
. After that you are good
until here.Quote:
-->
-->
, not
.
But mr fantastic told you the equation was separable. It is much easier to doQuote:
so that
. Integrating,
so that
.
Well, it is not hard to check yourself: ifQuote:
Which gives
Is this right?
then
while
. So
. No, that is not "3" and so your solution does not check.
No, the integral of 8 sin(x) is -8 cos(x).Quote:
Second:
integrating factor =} )
One of the things you should have learned long ago is thatQuote:
Thats about how far I can go, and don't know if its right.
Third:
Divide with
Thats how far I can go.
.
. Let u= y/3.