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Differential Equation Help!

Hello eve1,

The question is: x'(t) + [2/(1+t)]x(t) = 6, condition x(0) = 4. Find value of x(9).

I have done the following steps on the differential equation but have gone wrong somewhere as I cannot get the correct answer.

Could someone please check my steps and advice me on improvements?

Attached photo of working

Thanks

Me :smile: Differential equation.jpg
(edited 8 years ago)
Reply 1
Avatar for TeeEm
TeeEm
19
Original post by mathsRus
Hello eve1,

The question is: x'(t) + [2/(1+t)]x(t) = 6, condition x(0) = 4. Find value of x(9).

I have done the following steps on the differential equation but have gone wrong somewhere as I cannot get the correct answer.

Could someone please check my steps and advice me on improvements?

Attached photo of working

Thanks

Me :smile: Differential equation.jpg


your integrating factor should not have a minus in front of the integral on the exponential
Reply 2
Avatar for mathsRus
mathsRus
OP
8
Original post by TeeEm
your integrating factor should not have a minus in front of the integral on the exponential


Got it thanks!
Original post by mathsRus
Hello eve1,

The question is: x'(t) + [2/(1+t)]x(t) = 6, condition x(0) = 4. Find value of x(9).

I have done the following steps on the differential equation but have gone wrong somewhere as I cannot get the correct answer.

Could someone please check my steps and advice me on improvements?

Attached photo of working

Thanks

Me :smile: Differential equation.jpg


The differential equation is already in the correct form to use the integrating factor method you don't want to isolate the derivative on it's own.

The general form is y′+a(x)y=b(x) \displaystyle y'+a(x)y=b(x) and your IF would be
e∫a(x) dx \displaystyle e^{\int a(x)~dx}

:smile:

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