Solve x'+y=t y'-x=-t I am confused, and need some guidence! Please and Thanks
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Originally Posted by mandy123 Solve x'+y=t y'-x=-t I am confused, and need some guidence! Please and Thanks Differentiate the first again: $\displaystyle x''+y'=1$ so, substituting the second into the first: $\displaystyle x''+x=t+1$ and for $\displaystyle y$ you can differentiate the second and substitute the first. CB
Last edited by CaptainBlack; Apr 7th 2009 at 07:53 PM. Reason: corrected the typo
ok, but shouldn't it be x'' + x = 1 + t and then y'' + y = t - 1 what happened to the 1 in your first equation?
Originally Posted by mandy123 ok, but shouldn't it be x'' + x = 1 + t Mr F says: Yes. CB made a small mistake (he makes one every year). But it's the method that's important. and then y'' + y = t - 1 what happened to the 1 in your first equation? Your equations are correct and there should be no problem solving them.
Originally Posted by mandy123 ok, but shouldn't it be x'' + x = 1 + t and then y'' + y = t - 1 what happened to the 1 in your first equation? Typo now corrected. CB
so would my answer of x(t)=Acos(t) + Bsin(t) + 1 + t y(t)=Acos(t) + Bsin(t) - 1 + t be the right answer, or did i mess up somehow?
Originally Posted by mandy123 so would my answer of x(t)=Acos(t) + Bsin(t) + 1 + t y(t)=Acos(t) + Bsin(t) - 1 + t be the right answer, or did i mess up somehow? Do they work when you substitute them into the given pair of differential equations?
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