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antiseptic1488 [7]
3 years ago
10

I dont know this so please help me

Mathematics
2 answers:
Lemur [1.5K]3 years ago
5 0

a is 3k^2

b is -12k

and c is 12

loris [4]3 years ago
4 0
A.3k2
B.-12k
C.12
Yuh the answers for this
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Answer:

G.S=C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}

Step-by-step explanation:

We are given that non-homogeneous differential equation

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It is Cauchy Euler equation

Substitute x=e^t  x>0

Auxillary equation

D'(D'-1)-2=0

D'^2-D'-2=0

(D'-2)(D'+1)=0

D'-2=0 \implies D'=2

D'+1=0\implies D'=-1

Complementary solution

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Particular solution

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y_p=te^{2t}+\frac{1}{2}=x^2logx+\frac{1}{2}

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Hence, general solution G.S=C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}

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