00:01
In this question we are given a differential equation y double dash plus 3 y dash plus 2 y is equals to 0 and that y of 0 is equals to 1 and y dash 0 is equals to 0 to solve the ivp problem.
00:23
So this is what has been asked to us in the question.
00:26
So now let us focus on our solution.
00:28
So first of all let us create the characteristic equation.
00:32
It will be equals to lambda square plus 3 lambda plus 2 is equals to 0.
00:37
So this implies lambda plus 2 multiplied by lambda plus 1 is equals to 0.
00:43
So from here we get two values of lambda it is minus 1 and minus 2.
00:49
So we have this general solution as y is equals to e raised to the power minus lambda t.
00:54
This is the general solution.
00:57
So therefore we can say that y1 is equals to e raised to the power.
01:04
So here it is e raised to the power lambda t.
01:07
So we have minus t and y2 is equals to e raised to the power minus 2t...