Question

Simplify
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Answer 1

Auxiliary equation is (D−1)2(D2+1)y=0(D−1)2(D2+1)y=0

(D−1)2=0(D−1)2=0 or (D2+1)=0(D2+1)=0

D=1,1D=1,1 or D2=−1=i2D2=−1=i2

D=1,1D=1,1 or 0=±10=±1

Complementary function is

Yc=(C1+xC2)ex+eDx(C3cosx+C4sinx)Yc=(C1+xC2)ex+eDx(C3cos⁡x+C4sin⁡x)

Yc=(C1+xC2)ex+C3cosx+C4sinxYc=(C1+xC2)ex+C3cos⁡x+C4sin⁡x

0

[tex]Auxiliary equation is (D−1)2(D2+1)y=0(D−1)2(D2+1)y=0

(D−1)2=0(D−1)2=0 or (D2+1)=0(D2+1)=0

D=1,1D=1,1 or D2=−1=i2D2=−1=i2

D=1,1D=1,1 or 0=±10=±1

Complementary function is

Yc=(C1+xC2)ex+eDx(C3cosx+C4sinx)Yc=(C1+xC

Answer 2

Answer:

Simplify

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