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January 20th, 2014, 10:12 PM   #1
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complementary function & particular integral of a diff. equ.

Q. Find the complementary function & the particular integral of the following equation:
dy/dx = 2


I don't know how to calculate complementary function and particular integral of this problem. Please help.
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January 21st, 2014, 12:02 AM   #2
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Re: complementary function & particular integral of a diff.

dy/dx = 2
A particular solution is y=2x which is the result of a particular integal of 2*dx
The related homogeneous equation is dy/dx=0 which solutions are y=C , any constant.
The general solution is y=2x+C
Obviously, the undefined integration leads directly to the general solution.
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January 21st, 2014, 03:01 AM   #3
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Re: complementary function & particular integral of a diff.

Quote:
Originally Posted by JJacquelin
dy/dx = 2
A particular solution is y=2x which is the result of a particular integal of 2*dx
The related homogeneous equation is dy/dx=0 which solutions are y=C , any constant.
The general solution is y=2x+C
Obviously, the undefined integration leads directly to the general solution.
According to my book:

In case of linear differential equation with constant coefficient i.e. (dy/dx) + ay = b,

the complementary function

and the particular integral= b/a

Here a, b and A are constants.

I did understand the way you calculated the complementary function. But I couldn't understand how you calculated the particular integral. Could you please explain step by step?
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January 24th, 2014, 09:54 PM   #4
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Re: complementary function & particular integral of a diff.

ok, now I understand how you calculated the particular integral. Thanks a lot! My problem is solved now.
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