Turito Academy

Test Prep

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If <img src="data:image/png;base64,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" class="Wirisformula" alt="y equals e to the power of negative x end exponent left parenthesis A cos space x plus B sin space x right parenthesis" width="183" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«msup»«mi»e«/mi»«mrow»«mo»§#8722;«/mo»«mi»x«/mi»«/mrow»«/msup»«mo»(«/mo»«mi»A«/mi»«mi»cos«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»+«/mo»«mi»B«/mi»«mi»sin«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»)«/mo»«/math»'/> then y satisfies

Solution for the question - if y=e^(-x)(a cos x+b sin x) then y satisfies (d^(2)y)/(dx^(2))+2y=0 '/> (d^(2)y)/(dx^(2))+2(dy)/(dx)+2y=0 '/>(d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0 '/>