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y = c1 cos(3x) + c2 sin(3x) is a two-parameter family of solutions of the second-order DE y'' + 9y = 0. If possible, find a solution of the differential equation that satisfies the given side conditions. The conditions specified at two different points are called boundary conditions. (If not possible, enter IMPOSSIBLE.)

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okpalawalter8

Complete Question

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Answer:

The value is  [tex]y  =  5sin3x[/tex]

Step-by-step explanation:

From the question we are told that  

   [tex]y =  c_1\ cos3x + c_2 \  sin 3x[/tex]

given that y(0) =  0

We have that  

     [tex]c_1\ cos3(0) + c_2 \  sin 3(0)  =  0[/tex]

=>   [tex]c_1 =  0[/tex]

This means that

           [tex]y  =  c_2 \  sin 3x[/tex]

We also given that

          [tex]y[\frac{\pi}{6} ] =  5[/tex]

So  

         [tex]c_2  sin (3 *  \frac{\pi}{6} )  =  5[/tex]

=>    [tex]c_2  =  5[/tex]

Hence  

     [tex]y  =  5sin3x[/tex]

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