How to solve this equation y'''-4y"+2y'-16y=4x+1 using Method of Undetermined Coefficient, Variation of Parameters and Laplace Transformation

Line 2020-11-08 Answered

How to solve this equation y4y+2y16y=4x+1 using Method of Undetermined Coefficient, Variation of Parameters and Laplace Transformation

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Pohanginah
Answered 2020-11-09 Author has 96 answers

Solve:
The equation is y4y+2y16y=4x+1
Variation of Parameters:
The homogeneous equation is y4y+2y16y=0
The homogeneous solution is yh=c1e4.37796x+e0.18898x(c2cos(1.90236x)+c3sin(1.90236x))
Obtain the Wro
ians:
W=|eaxebxcoscxebxsincxaeaxbebxcoscxcebxsincxbebxsincxcebxcoscxa2eax(b2c2)ebxcoscx2bcebxsincx(b2c2)ebxsincx2bcebxcoscx|
W1=|0ebxcoscxebxsincx0bebxcoscxcebxsincxbebxsincxcebxcoscx1(b2c2)ebxcoscx2bcebxsincx(b2c2)ebxsincx2bcebxcoscx|
The values of a=4.37796,b=0.18898  and  c=1.90236
Further we have

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