Use the Laplace transform to solve y '' - 4y ' + 13y = d(t), y(0) = 0, y' (0) = 0 Q.B. Use Euler method with step size h=1/3 to find y(1) for the following differential equation y ' = x - xy - y, y(0)...

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Use the Laplace transform to solve y '' - 4y ' + 13y = d(t), y(0) = 0, y' (0) = 0 Q.B. Use Euler method with step size h=1/3 to find y(1) for the following differential equation y ' = x - xy - y, y(0) = -1 Q.C. Use the Laplace transform to solve y ' - 2y = te-t , y(0) = 1, (IF you do NOT use Laplace transform you will receive ZERO credit) Q.D. Use the Laplace transform to solve x ' = x - 3y, y' = -3x + y, x(0) = 1, y(0) = 1. (IF you do NOT use Laplace transform you will receive ZERO credit) Q.E Use the Laplace transform to solve y '' + 2y ' + 2y = cos(3t), y(0) = 1, y' (0) = 0. (IF you do NOT use Laplace transform you will receive ZERO credit) Make sure you SHOW and EXPLAIN ALL your steps. Otherwise ZERO credit will be assigned. ALL probems MUST be solved by methods presented in class. If you decide to use other methods or formulas you must explain and derive these.

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MA 2051 TEST II Term D, 2017 Q.A. Use the Laplace transform to solve '' ' ' y -4y +13y = d(t), y(0)=0,y(0)= 0 Q.B. Use Euler method with step size h=1/3 to ?nd y(1) for the following di?erential equation ' y = x- xy- y, y(0)=-1 Q.C. Use the Laplace transform to solve ' -t y -2y = te , y(0)=1, (IF you do NOT use Laplace transform you will receive ZERO credit) Q.D. Use the Laplace transform to solve ' ' x = x-3y, y =-3x+ y, x(0) = 1,y(0)=1. (IF you do NOT use Laplace transform you will receive ZERO credit) Q.E Use the Laplace transform to solve '' ' ' y +2y +2y =cos(3t),y(0)= 1, y(0)= 0. (IF you do NOT use Laplace transform you will receive ZERO credit) Make sure youSHOW and EXPLAIN ALL your steps. Otherwise ZERO credit will be assigned. ALL probems MUST be solved by methods presented in class. If you decide to use other methods or formulas you must explain and derive these. 1

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David answered on Dec 26 2021

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Use the Laplace transform to solve y '' - 4y ' + 13y = d(t), y(0) = 0, y' (0) = 0 Q.B. Use Euler method with step size h=1/3 to find y(1) for the following differential equation y ' = x - xy - y, y(0)...

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