00:02
Given, given y double dash plus 2 y dash minus 3 y equal to 0, y of 0 equal to 3, y dash 0 equal to minus 1, let y equal to e to the power mx be a trial solution, be a trial solution.
00:39
Then auxiliary, then auxiliary equation, equation that is a comma e will be, auxiliary equations will be m square plus 2m minus 3 equal to 0, that imply m square plus 3m minus m minus 3 equal to 0, that imply m plus 3 into m minus 1 equal to 0, therefore m equal to minus 3 comma m equal to 1.
01:31
Therefore, general solution, general solution, general solution equal to a e to the power x plus b e to the power minus 3x.
01:53
Now, now y of 0 equal to 3, 3, that imply 3 equal to a e to the power 0 plus b e to the power 0, so that imply a plus b equal to, this is first, this is first, so here that equal to y of x...