Find a particular solution to y4y16sec2tSolutionFirst findin

Find a particular solution to y+4y=16sec(2t).

First finding auxiliary equation

y\'\'+4y=-16sec(2x)
=m²+4=0
m=±2i

C.F.

y=acos2x+bsin2x

now find P.I.

y1=cos2x
y2=sin2x
Q= -16sec2x
W=y1y2\'y2y1\'

So W=2

P.I. =y1(y2*Q)/Wdx+y2(y1*Q)/Wdx

=cos2xsin2x(-8sec2x)dx+sin2xcos2x(-8sec2x)dx
=8cos2xtan2xdx-8sin2x1dx
P.I=4cos2x(lnsec2x)-8(sin2x)x

$Find a particular solution to y+4y=16sec(2t).SolutionFirst finding auxiliary equation y\'\'+4y=-16sec(2x) =m2+4=0 m=±2i C.F. y=acos2x+bsin2x now find P.I. y1=co$

Find a particular solution to y4y16sec2tSolutionFirst findin

Solution

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