Write the following linear differential equations with constant coefficients in the form of the linear system x˙=Ax and solve:(a)x¨+x˙−2x=0(b)x¨+x=0(c)dx¨−2x¨−x˙+2x=0Hint: Let x1=x,x2=x˙, etc.I have tried to do this in the following way but I do not know if I am doing well:Let x1=x,x2=x˙,x3=x¨,x4=x…, then the previous system becomes (a)x3+x2−2x1=0,(b)x3+x1=0,(c)x4−x3−x2+2x1=0and thus [x1x2x3x4]=[x23x2−x230]. Is this what it should be or is it different? Thank you very much.

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Lana Barlow · Accepted Answer

Let x1=x˙,x2=x¨,x3=dx¨. No need to substitute x as we want the final equations to be in the form of Ax. So  (x2+x1=2x),(x2=−x),(x3−2x2−x1=−2x):  Substituting x2 in the first equation, we get x1=3x. Finally, we substitute x1,x2 in the last equation and we get x3=−x. Now solve the final system  (x˙=3x),(x¨=−x),(x...=−x):

Write the following linear differential equations with constant coefficients in the form of the line

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