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 January 20th, 2014, 10:12 PM #1 Senior Member   Joined: Sep 2012 Posts: 112 Thanks: 0 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.
 January 21st, 2014, 12:02 AM #2 Senior Member   Joined: Aug 2011 Posts: 334 Thanks: 8 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.
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 $= Ae^-^a^x$

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?

 January 24th, 2014, 09:54 PM #4 Senior Member   Joined: Sep 2012 Posts: 112 Thanks: 0 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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