Question: solve full solution please. everything you need to answer the question is there(1)(20 points) Solve the following equations.(a)y'''-6y''+3y'-18y=0.(b)y''+8y'+41y=0.(c)y''+4y'+4y=8-12x.(d)y''-y'-2y=x3-1.(2)(20 points) Solve the following initial-value problems.(a)y''+2y'+y=x2,y(0)=1,y'(0)=0.(b)y''+4y'=et+e-4t,y(0)=2,y'(0)=0.(c)y''+2y'+5y=20sin(t),y(0)=0,y'(0)=2.

solve full solution please. everything you need to answer the question is there(1)(20 points) Solve the following equations.(a)y'''-6y''+3y'-18y=0.(b)y''+8y'+41y=0.(c)y''+4y'+4y=8-12x.(d)y''-y'-2y=x3-1.(2)(20 points) Solve the following initial-value problems.(a)y''+2y'+y=x2,y(0)=1,y'(0)=0.(b)y''+4y'=et+e-4t,y(0)=2,y'(0)=0.(c)y''+2y'+5y=20sin(t),y(0)=0,y'(0)=2.

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