Solve the following IVP for the second order linear equations y''-4y'+9y=0, y(0)=0, y'(0)=-8

Jerold 2021-01-10 Answered
Solve the following IVP for the second order linear equations
y4y+9y=0,  y(0)=0,  y(0)=8
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Expert Answer

Sadie Eaton
Answered 2021-01-11 Author has 104 answers

Given:
y4y+9y=0
y(0)=0
y(0)=8
The auxiliary equation of the givendifferential equation is
m24m+9=0
m=(4)+(4)2(4)(1)(9)2
=4±16362
=(4±i25)2
m=2±i5
Hence the general solution is
y=e2x(Acos5x+Bsin5x)
y(0)=0
0=1(A(1)+B(0))
A=0
y=e2x(Bsin5x)
y(0)=8
y=2ex(Bsin5x)+5ex(Bcos5x)
8=0+5(B)
B=85
Hence, the solution is
y=e2x(85sin5x)

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