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AQA FP3 Differential Equations Problem

Hello, this is the question,

Question.png

and this is the answer...

Answer.png


I do not understand why the particular integral is kx2ex and not kex

Thank you
Reply 1
Original post by NarutoUchiha
Hello, this is the question,

Question.png

and this is the answer...

Answer.png


I do not understand why the particular integral is kx2ex and not kex

Thank you


Because as they tell you in the question, ke^x would be part of the complementary function (solution of the homogeneous DE) so it can't be a PI when you have a non-zero term on the RHS.
Original post by NarutoUchiha
Hello, this is the question,

Question.png

and this is the answer...

Answer.png


I do not understand why the particular integral is kx2ex and not kex

Thank you


When the function on the right hand side is already a part of the complementary function then we have to multiply our usual trial solution by the variable.
So, since ex and xex e^x \mathrm{\ and\ }xe^x are both already present in the C,F
. then we must try kx2exkx^2e^x
Original post by davros
Because as they tell you in the question, ke^x would be part of the complementary function (solution of the homogeneous DE) so it can't be a PI when you have a non-zero term on the RHS.


Original post by brianeverit
When the function on the right hand side is already a part of the complementary function then we have to multiply our usual trial solution by the variable.
So, since ex and xex e^x \mathrm{\ and\ }xe^x are both already present in the C,F
. then we must try kx2exkx^2e^x



Thank You very much, i understand now! :smile:
Original post by NarutoUchiha
Thank You very much, i understand now! :smile:


You're welcome. Glad to help.

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