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actice Final Exam haileygray_Project2 - Googl COP_Project_2.pdf - Googl /553449/quizzes/1547338/take Question 7 0.5 pts Use the method of variation of parameters to find the general solution $ y(t) $ to the given differential equation given that the functions $ y_{1}(t)=6 t-1 $ and $ y_{2}(t)=e^{-6 t} $ are linearly independent solutions to the corresponding homogeneous equation for $ t>0 $. \[ t y^{\prime \prime}+(6 t-1) y^{\prime}-6 y=2 t^{2} e^{-6 t}, t>0 \] ? $ y(t)=c_{1}(6 t-1)+c_{2} e^{-6 t}-\frac{1}{32} t^{2} e^{-6 t}-\frac{1}{9} t^{3} e^{-6 t} $ ? $ y(t)=c_{1}(6 t-1)+c_{2} e^{-6 t}-\frac{1}{6} t^{2} e^{-6 t} $ ? $ y(t)=c_{1}(6 t-1)+c_{2} e^{-6 t}-\frac{31}{32} t^{2} e^{-6 t}-\frac{1}{9} t^{3} e^{-6 t} $ ? $ y(t)=c_{1}(6 t-1)+c_{2} e^{-6 t}-\frac{1}{32} t^{2} e^{-6 t} $ ? $ y(t)=c_{1}(6 t-1)+c_{2} e^{-6 t}-\frac{1}{6} t^{2} $ Question 8 0.4 pts Find $ \mathcal{L}^{-1}\left\{\frac{s}{(c-1)\left(c^{2}+1 c+12\right)}\right\}(t) $

          actice Final Exam
haileygray_Project2 - Googl
COP_Project_2.pdf - Googl
/553449/quizzes/1547338/take

Question 7

0.5 pts

Use the method of variation of parameters to find the general solution \( y(t) \) to the given differential equation given that the functions \( y_{1}(t)=6 t-1 \) and \( y_{2}(t)=e^{-6 t} \) are linearly independent solutions to the corresponding homogeneous equation for \( t>0 \).
\[
t y^{\prime \prime}+(6 t-1) y^{\prime}-6 y=2 t^{2} e^{-6 t}, t>0
\]
? \( y(t)=c_{1}(6 t-1)+c_{2} e^{-6 t}-\frac{1}{32} t^{2} e^{-6 t}-\frac{1}{9} t^{3} e^{-6 t} \)
? \( y(t)=c_{1}(6 t-1)+c_{2} e^{-6 t}-\frac{1}{6} t^{2} e^{-6 t} \)
? \( y(t)=c_{1}(6 t-1)+c_{2} e^{-6 t}-\frac{31}{32} t^{2} e^{-6 t}-\frac{1}{9} t^{3} e^{-6 t} \)
? \( y(t)=c_{1}(6 t-1)+c_{2} e^{-6 t}-\frac{1}{32} t^{2} e^{-6 t} \)
? \( y(t)=c_{1}(6 t-1)+c_{2} e^{-6 t}-\frac{1}{6} t^{2} \)

Question 8

0.4 pts

Find \( \mathcal{L}^{-1}\left\{\frac{s}{(c-1)\left(c^{2}+1 c+12\right)}\right\}(t) \)

$actice Final Exam haileygrayProject2 - Googl COPProject2.pdf - Googl /553449/quizzes/1547338/take Question 7 0.5 pts Use the method of variation of parameters to find the general solution y(t) to the given differential equation given that the functions y1(t)=6 t-1 and y2(t)=e^-6 t are linearly independent solutions to the corresponding homogeneous equation for t>0. t y^''+(6 t-1) y^'-6 y=2 t^2 e^-6 t, t>0 ? y(t)=c1(6 t-1)+c2 e^-6 t-(1)/(32) t^2 e^-6 t-(1)/(9) t^3 e^-6 t ? y(t)=c1(6 t-1)+c2 e^-6 t-(1)/(6) t^2 e^-6 t ? y(t)=c1(6 t-1)+c2 e^-6 t-(31)/(32) t^2 e^-6 t-(1)/(9) t^3 e^-6 t ? y(t)=c1(6 t-1)+c2 e^-6 t-(1)/(32) t^2 e^-6 t ? y(t)=c1(6 t-1)+c2 e^-6 t-(1)/(6) t^2 Question 8 0.4 pts Find ℒ^-1{(s)/((c-1)(c^2+1 c+12))}(t)$

Added by John D.

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