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# 1-a. For what values of k style="color:rgb(0,0,0);background-color:rgb(255,255,255);"> does the function y = cos(kt) satisfy the differential equation 9y'' = −25y? (Enter your answers as a comma-separated list.) k =?b. ) For those values of k, verify that every member of the family of functions y = A sin(kt) + B cos(kt) is also a solution. y = A sin(kt) + B cos(kt)    ⇒     y' = Ak cos(kt) − Bk sin(kt)    ⇒     y'' = −Ak2 sin(kt) − Bk2 cos(kt). The given differential equation 9y'' = −25y is equivalent to 9y'' + 25y =?thus, LHS = 9y'' + 25y= 9(−Ak2 sin(kt) − Bk2 cos(kt)) + 25( ? ) = −9Ak2 sin(kt) − 9Bk2 cos(kt) +( ? )   sin(kt) + 25B cos(kt) =(25 − 9k2)A sin(kt) +  ( ?)  cos(kt) =( ? )since k2 =( ?)

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