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[SOLVED] 23 solve initial value problem

karush

Well-known member
Jan 31, 2012
2,886
given #23
23p.PNG

so far
23.PNG

I could not get to the W|A solution before applying the y(0)=a


here is the book answer for the rest

23a.PNG
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
861
$e^{-2t/3} y' - \dfrac{2e^{-2t/3}}{3} y = \dfrac{1}{3}e^{-(3\pi+4)t/6}$

$\left(e^{-2t/3} y \right)' = \dfrac{1}{3}e^{-(3\pi+4)t/6}$

$e^{-2t/3} y = -\dfrac{2}{3\pi+4}e^{-(3\pi+4)t/6} + C$

$y = Ce^{2t/3} -\dfrac{2}{3\pi+4}e^{-\pi t/2}$
 

karush

Well-known member
Jan 31, 2012
2,886
mahalo
noticed there was 430+ views on this one