00:01
Hello everyone.
00:02
So here we are given with y double dash plus 5 squared y equal to k sine 16, y of 0 equal to 0, y dash of 0 equal to 0.
00:19
If y of pi by 2 equal to 3, then we have to find the value for k.
00:28
Now let us use the initial value problem to solve this.
00:33
Now to find the characteristics equation, we use r squared plus 5 squared is equal to 0.
00:42
So r squared will be equal to minus 5 squared, which is equal to minus 25.
00:49
So r will be equal to root of minus 25, which is equal to plus or minus 5i.
01:00
So therefore r we got plus 5i and minus 5i.
01:09
So using this we can write the characteristics equation yc, which is equal to c1 cos root 5x plus c2 sin minus root 5x.
01:25
Now we have to find yp to find the particular solution.
01:31
We can consider this as a cos 60 plus b sin 60.
01:38
So here y dash of p will be equal to 6a into minus sin 60 plus 6b cos 60.
01:51
So here again differentiating again we get y double dash of p will be equal to minus 36a cos 60 minus 36b sin 60...