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Particular solution
- Thread starter c4l3b
- Start date
D
Deleted member 4993
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c4l3b said:dx/dt = e^-t/2 + t^2 - 1
Find Particular solution which satisfies x(0) = 6
Your problem was discussed and answered at:
viewtopic.php?f=15&t=35264&p=136848#p136848
where are you stuck now?
Subhotosh Khan said:c4l3b said:dx/dt = e^-t/2 + t^2 - 1
Find Particular solution which satisfies x(0) = 6
Your problem was discussed and answered at:
viewtopic.php?f=15&t=35264&p=136848#p136848
where are you stuck now?
Do I integrate t^2 - 1....together or seperate i.e. only integrate t^2?
Because I have integrated t^2 as t^3/3 + c
D
Deleted member 4993
Guest
c4l3b said:Subhotosh Khan said:c4l3b said:dx/dt = e^-t/2 + t^2 - 1
Find Particular solution which satisfies x(0) = 6
Your problem was discussed and answered at:
viewtopic.php?f=15&t=35264&p=136848#p136848
where are you stuck now?
Do I integrate t^2 - 1....together or seperate i.e. only integrate t^2? <<< Does not matter - because all the "integration constants" (3 or 2 constants) will be added up to give you "single constant".
Because I have integrated t^2 as t^3/3 + c
D
Deleted member 4993
Guest
Solution:c4l3b said:Adding integrals together -2e^-t/2 + t^3/3.........is that right?......how do I impose the Part. solution x(0) =6? :|
Could you show me a systematic layout to solve equation?
x(t) = -2e[sup:s93hfkgw]-t/2[/sup:s93hfkgw] + 1/3*t[sup:s93hfkgw]3[/sup:s93hfkgw] - t + C
Initial condition ? x(0) = 6
x(0) = -2e[sup:s93hfkgw]-0/2[/sup:s93hfkgw] + 1/3*0[sup:s93hfkgw]3[/sup:s93hfkgw] - 0 + C
6 = -2 + C
C = 8
so the complete solution:
x(t) = -2e[sup:s93hfkgw]-t/2[/sup:s93hfkgw] + 1/3*t[sup:s93hfkgw]3[/sup:s93hfkgw] - t + 8