Solve the for the general solution of the differential equation (4D^{4}-4D^{3}-23D^{2}+12D+36)y=0

waigaK

waigaK

Answered question

2021-04-25

Solve the for the general solution of the differential equation
(4D44D323D2+12D+36)y=0

Answer & Explanation

toroztatG

toroztatG

Skilled2021-04-27Added 98 answers

Step 1
the equation's solution
(4D44D323D2+12D+36)y=0
It is clear that the auxiliary equation holds true with the help of synthetic division.
4m44m323m2+12m+36=0
(m2)2(2m+3)2=0   (Facr)
m2=0 or m2=0 or 2m+3=0 or 2m+3=0
(Set each factor equal to 0)
m=2 or m=2 or m=32 or m=32
Step 2
Whose roots m=2,2,32,32 may be obtained by synthetic division. Then the general solution is seen to be
y=(c1+c2x)e2x+(c3+c4x)e3x2
Therefore the solution is y=(c1+c2x)e2x+(c3+c4x)e3x2

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