00:01
In this problem we are given that y triple dash equals to 18 times x, y double dash at 0 equals to 12, y dash at 0 equals to 3 and y at 0 equals to 7.
00:20
And we are asked to find out the value of y.
00:23
So first let us integrate y triple dash equals to 18 times x on both the sides.
00:32
So here we get y double dash equals to 18 times x squared over 2 plus the constant c1 of integration.
00:48
Here 2 and 18 get cancelled 9 times.
00:51
So we have y double dash to be equal to 9 times x squared plus constant c1.
00:57
So now let us make use of the initial condition y double dash of 0 equals to 12.
01:04
To find out the value of c1.
01:07
So, substituting x as 0, we have y double dash of 0 equals to 9 times 0 squared plus the constant c1, which implies that 12 equals to the constant c1 since 9 times 0 squared is 0 itself.
01:25
So substituting back this value of c1, we get y double dash equals to 9 times x squared plus 12.
01:35
So now let us integrate this equation again.
01:40
So integrating on both sides, we get y -dash equals to 9 times x -cubed over 3 plus 12 times x plus the constant c2 of integration.
01:57
So now here it can be seen that 3 and 9 get cancelled 3 times.
02:01
So we have y -dash to be equal to 3 times x cubed plus 12 times x -x plus the.
02:07
Constant c2...