00:01
Hi, given d square y by d x square minus 3 into dy by d x minus 4y is equal to 0, also given the initial value condition, y of 0 is equal to a and y dash of 0 is equal to minus 15.
00:22
Writing this equation in the d form we have d square minus 3d minus 4 into y is is equal to 0.
00:33
Taking the auxiliary equation we have m square minus 3m minus 4 is equal to 0 which implies m minus 4 into m plus 1 is equal to 0 which gives m is equal to 4 comma minus 1.
00:59
Therefore, we have y of t is equal to c1 e rise to the par 4 t plus c2 e rise to the par minus t.
01:12
Now given the condition, y of 0 is equal to a, implies c1 e rise to the par 0 plus c2 e rise to the par 0 is equal to a, which implies c1 plus c2 is equal to a.
01:33
Solving for c1 gives c1 is equal to a minus c2.
01:39
Also given y dash of 0 is equal to minus 15.
01:46
D differentiating y of t with respect to t, we have, y dash is equal to 4 c1 e rise to the power 4t minus c2 e rise to the power...