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# Differential Equation - Complimentary function and particular integral

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1. Can anyone help with the below question, just can't get my head around it. Thank you.

Use the method of complimentary function and particular integral to find theparticular solution of the differential equationy''+5y'+4y=sinx , with y(0)=1 and y' (0)=2
2. (Original post by Jake Brookes)
Can anyone help with the below question, just can't get my head around it. Thank you.

Use the method of complimentary function and particular integral to find theparticular solution of the differential equationy''+5y'+4y=sinx , with y(0)=1 and y' (0)=2
This looks to be a standard question. What have you tried?
3. As it has been said, it looks quite standard.

You get the complementary function by first finding the solutions of the auxiliary equation: .

The particular integral can be found by using and subbing that into the oringal equation.

Combining the complimentary function and the particular integral gives the general solution. The known values can then be used to find the values of the unknown constants.
4. (Original post by NeverLucky)
As it has been said, it looks quite standard.

You get the complementary function by first finding the solutions of the auxiliary equation: .

The particular integral can be found by using and subbing that into the oringal equation.

Combining the complimentary function and the particular integral gives the general solution. The known values can then be used to find the values of the unknown constants.

y = Ae^(-4 x)+Be^(-x)+1/8 sin(x)-1/8 cos(x) is what I got
5. bump
6. (Original post by Jake Brookes)
bump
bump doesnt do ****

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