Differential Equations Textbook wrong!  

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My textbook on differential equations has had me confused for the last few days and had me getting questions wrong all because today I found they made a typo! If you're using the OCR MEI textbook for the DE Module please note the following...

pg. 94- Special cases "CH7 linear equations with constant coefficients"

The book is explaining that when you're solving a non homogeneous linear DE and your complementary function is of the same form as the right hand side of your equation you have to multiply your trial function by your independant variable. Right this is of course correct and ok. However the example they gave made it look to me like if your complementary function has an exponential, no matter what the power you must alter your trial function. This of course (now I know) not the case! You only alter the trial function if the power in the exponential of your R.H.S is the same as one of your trial functions!!!

e.g.

Complementary= Ae3x+Be2x 

R.H.S= 7e2x

Then YES make your trial function cxe2x

But the book gave an example where they incorrectly worked out the complementary function to be:

Ae2x+Be2x  with, R.H.S 3e3x

And still altered the trial function! This really confused me and made me believe that the trial function is changed if the complementary function contains just the same form (type of function trig, exp, log) as the R.H.S. This is not the case the coefficient of x, or whatever the variable is, must be the same for you to change the trial function.

Just wanted to clarify this if anyone had the same problem!

PlanckTime - Amin

Oh nice the differences are relatively subtle but I can see why you were originally slightly confused by my terminology. That book sounds super useful, could you post an amazon link or something?

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Your terminology confused me, but I managed to figure out what you meant by this. I have a calculus book called "Problem Solvers: Calculus", which makes a basic sign error. I also find many times, even within the same problem, they change what the integral sign looks like, or just change the entire font sometimes. Although, it still is a very good book despite the mistakes!

That one guy that's always on

 
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Awesome, I may look into getting that book, is it useful at all for calculus past A level/ AP so uni level?

Also I would love to know your terminology for the following:

  • Auxiliary Equation (Equation in terms of λ)
  • Particular Integral (the bit you add on to solve non homogeneous DEs)
  • Complementary function (solution to the non homogeneous equation when its made homogeneous- by neglecting the right hand side)

PlanckTime - Amin

It goes into very advanced calculus and differential equations (such as the gamma function, elliptical integrals, and frobenius series). It also goes into solving for differentials, fluid forces/pressure, electricity, and applied differential equations. 

I call the auxiliary equation the auxiliary equation (except I use "m" instead of  λ), the particular integral the particular solution, and the complementary function the homogeneous solution.

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