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May 14th, 2018, 05:58 AM   #1
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Differential Equations

I have attached the question images Q43 & Q44. These are my previous year questions, which I was unable to solve. Kindly help me.
Thank you
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May 14th, 2018, 06:31 AM   #2
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Why don't you just plug the different solutions into the equation and see whether you get a correct result?
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May 14th, 2018, 09:10 AM   #3
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That's certainly the most direct approach.

I think that the first question has an error. None of them look like solutions. I suspect the second also has an error, but it does at least have a solution.
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May 15th, 2018, 09:18 PM   #4
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Quote:
Originally Posted by Micrm@ss View Post
Why don't you just plug the different solutions into the equation and see whether you get a correct result?
Q43. I'm getting the general solution as c1e^(2+sqrt(3))x + c2e^(2-sqrt(3))x
But I'm not sure what else needs to be done to derive one of the solutions given.
Q44. I have substituted the solutions in the D.E and I'm getting option A & B as solutions. Is it correct ?

Last edited by Lalitha183; May 15th, 2018 at 09:59 PM.
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May 15th, 2018, 11:07 PM   #5
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No.
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May 16th, 2018, 03:03 AM   #6
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The characteristic equation for 43 is . r= 0 is a root. so that and [tex]r= -2- \sqrt{3}[tex] are the other 2 roots.

The general solution to the differential equation is . You forgot the constant solution.

For 44 if you set y= x, then y'= 1 and y''= 0 so the equation becomes x(0)- 1+ 1= 0. If y= sin(x+ c) then y'= cos(x+ c) and y''= -sin(x+ c). The equation becomes . If y= sinh(x+ c) then y'= cosh(x+ c) and y''= sinh(x+ c). The equation becomes [tex]sinh^2(x+ c)- cosh^2(x+ c)+ 1= 0.
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