Question

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.)

Answer 1

Complete Question

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Answer:

The value is  $y = 5sin3x$

Step-by-step explanation:

From the question we are told that  

   $y = c_1\ cos3x + c_2 \ sin 3x$

given that y(0) =  0

We have that  

     $c_1\ cos3(0) + c_2 \ sin 3(0) = 0$

=>   $c_1 = 0$

This means that

           $y = c_2 \ sin 3x$

We also given that

          $y[\frac{\pi}{6} ] = 5$

So  

         $c_2 sin (3 * \frac{\pi}{6} ) = 5$

=>    $c_2 = 5$

Hence  

     $y = 5sin3x$