00:01
In this question we have a differential equation y double prime plus 3y prime is equals to 4x minus 5 we are required to solve this differential equation by using undetermined coefficients so let's see how to solve this question first of all let's apply the differential operators so we can write b squared plus 3d into y is equals to 4x minus 5 and now the auxiliary equation for left -hand side equation can be written as m squared plus 3m is equal to 0.
00:47
Therefore, this will be equal to m into m plus 3 is equal to 0.
00:54
Hence, m 1 is equal to 0 and m2 is equal to minus 3.
01:01
So based on this the complementary function yc will be equals to c1 plus c2, a to the power minus 3x.
01:13
Now, since 4x minus 5 is annihilated by differential operator d square, therefore apply the differential operator d square to both sides of the given equation.
01:25
So we can write d squared multiplied by d square plus 3d into y is equal to d square into 4x minus 5.
01:39
This will be equal to 0.
01:43
Now the auxiliary equation corresponding to this equation will be equals to m squared multiplied by m square plus 3m is equal to 0.
01:56
From these two terms we can take out m as a common.
02:00
So we will have m cube multiplied by m plus 3 is equal to 0...