Question

1) ?1(?) = 5 , ?2(?) = sin2 ? y ?3(?) = cos2 ? (−∞,∞) it...

1) ?1(?) = 5 , ?2(?) = sin2 ? y ?3(?) = cos2 ? (−∞,∞) it is linearly dependent or independent.

2)Determine the Wronskian of the Function Set   
?1(?) = ?2 y ?2(?) = 1 − ?2, ?3(?) = 2 + ?2 (−∞,∞)

3) Be a solution of the differential equation?2?′′ − 3??′ + 5? = 0
Find a second solution using the order reduction formula.

4) Find the general solution of the differential equation.
    ?′′′ + 3?′′ + 3?′ + ? = 0

5) Solve the initial value problem
  ?′′ − 2?′ + ? = 0, ?(0) = 5,?′(0) = 10

6)Find the general solution of the differential equation by the method of indeterminate coefficients 
 ?′′ − 2?′ - 2y = sin2x

7) Use the parameter variation method to solve the equation

?′′ − 9? = 9?/??

8) Solve the differential equation by the parameter variation method

?′′ + ? = ????

9) Solve the following Cauchy -Euler differential equation by the variation method

?2?′′ − 2??′ + 2? = ?4??

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