SOLUTION: Solve the equation d^3y/dx^3 +2d^2 y/dx^2 -13dy/dx +10y=0 ? (5marks)

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Question 1025057: Solve the equation
d^3y/dx^3 +2d^2 y/dx^2 -13dy/dx +10y=0 ? (5marks)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
d%5E3y%2Fdx%5E3+%2B2d%5E2y%2Fdx%5E2+-13dy%2Fdx+%2B10y=0+
Using the D-notation, the differential equation becomes
%28D%5E3%2B2D%5E2-13D%2B10%29y+=+0
<==> (D-2)(D-1)(D+5)y = 0, after factorization

==>the general solution is
highlight%28y+=+Ae%5E%282x%29+%2B+Be%5Ex+%2B+Ce%5E%28-5x%29%29