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 June 9th, 2019, 04:50 AM #1 Senior Member   Joined: Dec 2015 From: Earth Posts: 836 Thanks: 113 Math Focus: Elementary Math Equation : $\displaystyle y’’=y$. Add both sides +y’ then substitution as $\displaystyle y’+y=t$. $\displaystyle t’=t$. Is this way correct? Last edited by skipjack; June 9th, 2019 at 11:18 AM.
 June 9th, 2019, 06:25 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,649 Thanks: 1476 The usual way is to form the characteristic equation. $y''-y=0$ $s^2 - 1= 0$ $s = \pm 1$ $y = c_1 e^t + c_2 e^{-t}$ Thanks from topsquark and idontknow
 June 9th, 2019, 09:08 AM #3 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,849 Thanks: 661 Math Focus: Yet to find out. Also the chant "what when differentiated twice equals itself!" Thanks from idontknow
June 9th, 2019, 11:02 AM   #4
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Quote:
 Originally Posted by Joppy Also the chant "what when differentiated twice equals itself!"
I don't remember hearing that one down the pub.

June 9th, 2019, 11:24 AM   #5
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Quote:
 Originally Posted by idontknow Is this way correct?
Yes. Having found $t$, you could then solve $y' + y = t$ by using an integrating factor.

The same integrating factor works for the original equation.

Integrating $e^xy'' - e^xy = 0$ gives $e^xy' - e^xy = \text{A}$, etc.

June 9th, 2019, 03:40 PM   #6
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 Originally Posted by romsek I don't remember hearing that one down the pub.
Apparently you go to the wrong bars.

-Dan

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