00:01
In this version, part 2, we have our equation as y -dash, double dash, minus 2 y -dash plus 9 -1 is equal to 0.
00:13
So this implies us as 0 squared minus 2 t plus 9 is equal to 0.
00:20
So now our correctistic equation, which is so m squared minus 2m plus 9 is equal to good.
00:31
Now bear here, r2 for m, will be equal to 2 plus minus square root of 0 minus 3 sigma divided by 2.
00:46
And this will be as m is equal to 2 plus minus, this is 36 square root of 32 iota minus minus 1 stands for iota here divided by 2.
01:04
So we will get r value for m as equal to 2 plus minus 4 root 2 iota divided by 2.
01:17
So m will be equal to 1 plus minus 2 root 2 iota.
01:25
And here the general solution solution will be as c1, b to the power of minus 1 plus 2 root 2.
01:43
2 iota x plus c2 e to the power of minus 1 minus 2 root 2 iota x so we can write it as e to the part of x within the bracket c1 cos 2 root 2 x plus c2 sine 2 roof 2 x and this will be our answer for a part.
02:21
And now let's verify our course solution.
02:26
So verification as y of x is equal to e to the power of x c1 cost 2 root 2 x plus 2 c2 sine 2 root 2 x.
02:50
This will be taken as equation 1 and y dash x will be e to the power of x c1 cost 2 root 2 x plus c2 sine 2 root 2 x plus e to the power of x minus 2 root 2 c2 sine 2 root 2 x plus 2 cause 2 root 2 x so by equation 1 we can say y dash x is equal to y dash x and if we take this part as a so y -dash x plus a and we will take this as equation 2 so now y double dash x will be as equal to y dash x plus e to the power of x minus 2 root 2 c2 sine 2 root 2 x plus 2 root 2 c2 cost x 2 root 2 2 2 2 2 2 added by e to the power of x minus 8 c2 cost 2 root 2 x plus 8 c2 sine 2 under root 2 x x and this implies as y double dash x is equal to y dash x plus e to the power of x minus 2 root 2 c2 sine 2 root 2 x plus 2 root 2 c2 cost 2 root 2 x plus minus e to the bar of x plus minus e to the bar of x plus minus e to the bar of x.
05:10
8 c1 cost 2 under root 2 x minus 8 c2 sine 2 under root 2 x 5 now by equation 2 and 1 we will get r when before y double dash x is equal to y dash x plus y dash x minus y -dash x minus y -x minus 8y x so here y double dash x will be equal to y double dash x minus 2 y dash x plus 9y x is equal to 0 and this is similar to the given equation so this is the given order is existing here so hence verified verified answer 8.
06:15
So this is our first complete solution of part 8.
06:19
Now in the part b of the same portion we have to solve here y double dash minus 1 by 3 y dash y -dash y -is equal to 0.
06:30
So our characteristic equation equation for this is m squared minus 1 upon 9 is equal to 0 and therefore our value for m will be equal to plus minus 1 upon 3 so here we have our value for m which is plus minus 1 apart 3 here this is the answer for part p also we can verify this so let's move on with the part question 5 so for solution of this part we have y is equal to c1 plus c2 t t e to the power of 4 t and this will be our equation 1 so again if you y dash t is equal to 4 e to the power of 4 t c2 plus c2 t plus e to the power of 4 t plus c2 so this implies us as y 1 y dash is equal to 4 y dash y -dash is equal to 4 y plus c2 e to the part of 4 t and now we will take this as equation true so therefore y double dash will be 4 y dash plus 4 c2 e to the part of 4 t by equation 2 so y double dash is equal to 4 y dash plus 4 y dash minus 4 y.
08:18
This will give us 5 double dash is equal to 4 y dash plus 4 y dash minus 16 y...