(adsbygoogle = window.adsbygoogle || []).push({}); 1. Given i. dx/dt + y = 0; x(0) = 1 : ii. dy/dt + x = 0; y(0) = 0 Solve for the solns of x and y

Although these are first order dif eq's I worked them as leading to a second order undetermined coefficients problem

First I wrote them as

i. x' + y = 0 and ii. y' + x = 0

Eqn. ii leads to y' = -x and this to y'' = -x' => -y" = x' substitute back in i. for -y" + y = 0

=> -y" + 0y' + y = 0 now to solve i in it's new form of a 2nd order eqn.

I began by writing as y" -0y'-y=0 and if std form is y''+ay'+by then a=0, b=-1 and a^2 = 0 4b = -4 => a^2 >4b and soln is form of x=C1e^-r1x + C2e^r2x the values for r1 and r2 are calculated from y" + 0y' + y = 0 or r^2 - 1 =0 so r = +/- 1. the soln then becomes x = C1e^x + C2e^-x. Now applying initial value conditions x(0) = 1 => 1 = C1 + C2

I then complete the other half of the problem similarly and end with 0 = C1 + C2

and I'm stuck. Can someone please point out where I'm going wrong?

thanks

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# Homework Help: Diff eq problem appears simple but is deadly

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