00:01
So, y double dash minus 4 y dash is equals to 8 x square plus 2 e power 3 x.
00:10
This is equation number 1.
00:12
So the auxiliary equation is r square minus 4 r equals to 0.
00:25
So r r minus 4 equals to 0.
00:29
So the value of r equals to r 0 comma 4.
00:35
So complementary function is y is equals to c1 plus e2 e c2 c2 e to the power 4 x.
00:54
This is the complementary function.
00:57
And now as o is a root of auxiliary, is root of auxiliary equation.
01:14
So y p is equals to x ax square plus bx plus c plus d e power 3 x.
01:34
So y p dash is equals to 3 ax square plus 2 bx plus c plus 3 d e 3 x.
01:46
So y p double dash is equals to 6 ax plus 2 b plus 9 d e 3 x.
01:58
So substituting substituting y y double dash in equation 1.
02:20
So we get 6 ax plus 2 b plus 9 3 x minus 4 e ax square plus 2 bx plus e plus plus c plus 3 d e x is equals to 8 x square plus 2 e 3 x...