00:01
In this problem we have to solve the given boundary value problem.
00:05
So the differential equation is here.
00:08
Y double dash minus 14 y -dice plus 49y equal 0.
00:19
And the boundary condition is given y 0 equal 1 and y 1 equal 0.
00:28
So to find the boundary value solution of the boundary value problem, first we have to find the general solution so for that we have to find the characteristic roots so for that we will write characteristic equation so this is equal to r square minus 14r plus 49 equal 0 how to find the root of this equation we have r minus 7 whole square equal 0 so we have r equal 7 7 7 7 so this is the characteristic root which are repeated.
01:15
Now the general solution can be written as the general solution is yx equal c1, e to power 7x or 7 and plus c2x e to power 7x.
01:37
So this is the general solution which further can be written as yx equal c1 plus c1.
01:45
C2x into e to power 7x.
01:51
So this is yx.
01:53
Now to find this arbitrary constraints, c1 and c2, we will use this boundary conditions.
02:01
So first we have y0 equal 1.
02:04
So putting x equal 0 here, we have y 0 equal c1 plus c2 into 0 and e to power 7 that is 0...
