Question Easy calculus question. I will rate and like. Thank you. Which of the following is a solution to the second order differential equation y" = -4y?To answer this question:• Check whether each of the following proposed solutions satisfies the given differential equation.• You'll need to take the second derivative of each function.a. y = sin 2tb. Y = -t3%3DC. Y = cos 2td. y = e2ty"e. Y =a and cdb and eall of thesenone of these
QZQS1C The Asker · Calculus
Easy calculus question. I will rate and like. Thank you.
Transcribed Image Text: Which of the following is a solution to the second order differential equation y" = -4y?To answer this question:• Check whether each of the following proposed solutions satisfies the given differential equation.• You'll need to take the second derivative of each function.a. y = sin 2tb. Y = -t3%3DC. Y = cos 2td. y = e2ty"e. Y =a and cdb and eall of thesenone of these
More Transcribed Image Text: Which of the following is a solution to the second order differential equation y" = -4y?To answer this question:• Check whether each of the following proposed solutions satisfies the given differential equation.• You'll need to take the second derivative of each function.a. y = sin 2tb. Y = -t3%3DC. Y = cos 2td. y = e2ty"e. Y =a and cdb and eall of thesenone of these
Community Answer
PBFC7J
Step 1Given differential equation is y"=-4yStep 2It con be written asy^('')+4y=0a.) y=sin 2t{:[" LHS "{:=y^('')+4y=(d)/(dt)((d)/(dt)(sin 2t)))+4(sin 2t)],[=(d)/(dt)(2cos 2t)+4sin 2t],[=-4sin 2t+4sin 2t=0=" RHS "]:}Hencey= sinet is a solution of given equation.{:[y=-(2)/(3)t^(3)],[:.y^('')=(d)/(dt)(-(2)/(3)xx3t^(2))=(d)/(dt)(-2t^(2))=-4t],[" LHs "=-4t+4(-(2)/(3)t^(3))=-4t-(8)/(3)t^(3)!=0],[:.y=-(2)/(3)t^(3)" is not a sulution of "]:}b ) give ... See the full answer