How to solve this equation y−4y+2y−16y=4x+1 using Method of Undetermined Coefficient, Variation of Parameters and Laplace Transformation
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Solve:The equation is y‴−4y″+2y′−16y=4x+1Variation of Parameters:The homogeneous equation is y‴−4y″+2y′−16y=0The homogeneous solution is yh=c1e4.37796x+e−0.18898x(c2cos(1.90236x)+c3sin(1.90236x))Obtain the Wroians:W=|eaxebxcoscxebxsincxaeaxbebxcoscx−cebxsincxbebxsincx−cebxcoscxa2eax(b2−c2)ebxcoscx−2bcebxsincx(b2−c2)ebxsincx−2bcebxcoscx|W1=|0ebxcoscxebxsincx0bebxcoscx−cebxsincxbebxsincx−cebxcoscx1(b2−c2)ebxcoscx−2bcebxsincx(b2−c2)ebxsincx−2bcebxcoscx|The values of a=4.37796,b=−0.18898 and c=1.90236Further we have<
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