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Lecture 7 Notes

# Lecture 7 Notes - Today Reminder midterm next week Chapter...

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Today • Reminder - midterm next week! Chapter 1.1-1.3, 2.1-2.4, 3 (not 3.6) • Finish up undetermined coefficients • Physics applications - mass springs • Undamped, over/under/critically damped oscillations

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Method of undetermined coefficients (3.5) Example 6. Find the general solution to . • What is the form of the particular solution? (A) (B) (C) (D) (E) Don’t know / still thinking. y 4 y = t 3 y p ( t ) = At 3 y p ( t ) = At 3 + Bt 2 + Ct + D y p ( t ) = At 3 + Bt 2 + Ct y p ( t ) = At 3 + Bt 2 + Ct + D + Ee 2 t + Fe 2 t
Method of undetermined coefficients (3.5) Example 6. Find the general solution to . • What is the form of the particular solution? (A) (B) (C) (D) (E) Don’t know / still thinking. y 4 y = t 3 y p ( t ) = At 3 y p ( t ) = At 3 + Bt 2 + Ct + D y p ( t ) = At 3 + Bt 2 + Ct y p ( t ) = At 3 + Bt 2 + Ct + D + Ee 2 t + Fe 2 t

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Method of undetermined coefficients (3.5) Example 6. Find the general solution to . • What is the form of the particular solution? (A) (B) (C) (D) (E) Don’t know / still thinking. y + 2 y = e 2 t + t 3 y p ( t ) = Ae 2 t + Be 2 t + Ct 3 + Dt 2 + Et + F y p ( t ) = Ae 2 t + Bt 3 + Ct 2 + Dt y p ( t ) = Ae 2 t + Bt 3 + Ct 2 + Dt + E y p ( t ) = Ae 2 t + ( Bt 4 + Ct 3 + Dt 2 + Et )
Method of undetermined coefficients (3.5) Example 6. Find the general solution to . • What is the form of the particular solution? (A) (B) (C) (D) (E) Don’t know / still thinking. y + 2 y = e 2 t + t 3 y p ( t ) = Ae 2 t + Be 2 t + Ct 3 + Dt 2 + Et + F y p ( t ) = Ae 2 t + Bt 3 + Ct 2 + Dt y p ( t ) = Ae 2 t + Bt 3 + Ct 2 + Dt + E y p ( t ) = Ae 2 t + ( Bt 4 + Ct 3 + Dt 2 + Et )

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Method of undetermined coefficients (3.5) Example 6. Find the general solution to . • What is the form of the particular solution? (A) (B) (C) (D) (E) Don’t know / still thinking. y + 2 y = e 2 t + t 3 y p ( t ) = Ae 2 t + Be 2 t + Ct 3 + Dt 2 + Et + F y p ( t ) = Ae 2 t + Bt 3 + Ct 2 + Dt y p ( t ) = Ae 2 t + Bt 3 + Ct 2 + Dt + E y p ( t ) = Ae 2 t + ( Bt 4 + Ct 3 + Dt 2 + Et ) y p ( t ) = Ae 2 t + t ( Bt 3 + Ct 2 + Dt + E )
Method of undetermined coefficients (3.5) Example 6. Find the general solution to . • What is the form of the particular solution? (A) (B) (C) (D) (E) Don’t know / still thinking. y + 2 y = e 2 t + t 3 y p ( t ) = Ae 2 t + Be 2 t + Ct 3 + Dt 2 + Et + F y p ( t ) = Ae 2 t + Bt 3 + Ct 2 + Dt y p ( t ) = Ae 2 t + Bt 3 + Ct 2 + Dt + E For each wrong answer, for what DE is it the correct form? y p ( t ) = Ae 2 t + ( Bt 4 + Ct 3 + Dt 2 + Et ) y p ( t ) = Ae 2 t + t ( Bt 3 + Ct 2 + Dt + E )

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Method of undetermined coefficients (3.5) Example 6. Find the general solution to . • What is the form of the particular solution? (A) (B) (C) (D) (E) Don’t know / still thinking. y 4 y = t 3 e 2 t y p ( t ) = ( At 3 + Bt 2 + Ct + D ) e 2 t y p ( t ) = ( At 3 + Bt 2 + Ct ) e 2 t y p ( t ) = ( At 3 + Bt 2 + Ct ) e 2 t +( Dt 3 + Et 2 + Ft ) e 2 t y p ( t ) = ( At 4 + Bt 3 + Ct 2 + Dt ) e 2 t
Method of undetermined coefficients (3.5) Example 6. Find the general solution to . • What is the form of the particular solution? (A) (B) (C) (D) (E) Don’t know / still thinking. y 4 y = t 3 e 2 t y p ( t ) = ( At 3 + Bt 2 + Ct + D ) e 2 t y p ( t ) = ( At 3 + Bt 2 + Ct ) e 2 t y p ( t ) = ( At 3 + Bt 2 + Ct ) e 2 t +( Dt 3 + Et 2 + Ft ) e 2 t y p ( t ) = ( At 4 + Bt 3 + Ct 2 + Dt ) e 2 t

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Method of undetermined coefficients (3.5) Example 6. Find the general solution to .
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