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Sagot :
The general solution of the given higher-order differential equation. y''' − 9y'' 15y' 25y = 0 is Y= c1e^-x +c2e^5x + c3xe^5x
m^3 -9m^2+15m+25=0
Possible rational roots = 1,-1,5,-5,25
Now on putting these possible rational roots which have been found by the discriminant and hit and trial method,
we will check these roots.
m=-1 comes out to be a root of the equation.
m^2-10m+25=0
(m-5)(m+5)=0
(m-5)^2=0
m=5
So the general equation comes out to be
Y= c1e^-x +c2e^5x + c3xe^5x
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