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Second order differential equations FP3 AQA question

I have attached the question in the post. Here is what I have done so far.

Let

y=e^{mx}

And I got the auxiliary equation of

m^2 -4m +3=0

Therefore

m=1, 3

So the complimentary function is

y=Ae^{x}+Be^{3x}

So the overall general solution would be

y=Ae^{x}+Be^{3x}+Cx+D

I just don't know how to get the particular integral and particular solution. Help please?

image.jpg29.4KB

Reply 1

Robbie242

Original post by CharlieBoardman

I have attached the question in the post. Here is what I have done so far.

Let

y=e^{mx}

And I got the auxiliary equation of

m^2 -4m +3=0

Therefore

m=1, 3

So the complimentary function is

y=Ae^{x}+Be^{3x}

So the overall general solution would be

y=Ae^{x}+Be^{3x}+Cx+D

I just don't know how to get the particular integral and particular solution. Help please?

Let our particular integral be of the form

y=\lambda x+\mu

(1) (since our differential equation is equal to 6x-5) where

\lambda, \mu

are constants. Also your C.F is just

y=Ae^{x}+Be^{3x}

work separately and then combine the particular integral and complimentary function to gain a general solution

Differentiate this expression (1) once, and then again to then be plugged back into our initial differential equation to find out the values of

\lambda

and

\mu

(edited 10 years ago)

Reply 2

natninja

Original post by CharlieBoardman

I have attached the question in the post. Here is what I have done so far.

Let

y=e^{mx}

And I got the auxiliary equation of

m^2 -4m +3=0

Therefore

m=1, 3

So the complimentary function is

y=Ae^{x}+Be^{3x}

So the overall general solution would be

y=Ae^{x}+Be^{3x}+Cx+D

I just don't know how to get the particular integral and particular solution. Help please?

To find the particular integral you should let y=Cx+D and substitute into the original differential equation.

Then to find your particular solution you should simply apply the boundary conditions to your solution and d/dx of your solution.