With reduction of order, we assume a solution of the form
, with
. Then
and substituting into the ODE gives
Let
, so that
. This gives the linear ODE
This equation is also separable, so you can write
Integrating both sides with respect to
gives
Next, solve
for
by integrating both sides again with respect to
.
And finally, solve for
.
and note that
is already taken into account as part of
, so this is the general solution to the ODE.
12/3 is 4 so multiply each by 4 so 7.79 x 4 is 31.16 5.68x4 22.72 13.99x4 55.96
31.16 + 22.72+ 55.96
Answer: $109.84
Answer:
no solution
Step-by-step explanation:
Answer:
Step-by-step explanation:
If we look, "y" can be factored out of the entire expression because it goes into them all. This gives y(2x^3 - 4x^2 + 8x - 16)
Since everything inside the brackets is a multiple of 2 we can factor it out.
2y (x^3 - 2x^2 + 8x - 16)
Here to factor (x^3 - 2x^2 + 8x - 16) we could either use a calculator, or notice that when we subsitute 2 into the equation, it equals 0. Therefore (x - 2) must be a factor. The other factor must be (x^2 + 8) because:
(x - 2) ( )
We need to have 1 x^3 so we know the first part of the factor must be x^2
The also need to have -16 when we multiply this out, -2 * something equals -16. Meaning we must have 8 inside of the brackets.
This gives :
(x - 2) (x^2 + 8).
When we expand this out we get (x^3 - 2x^2 + 8x - 16)
Therefore in total we have
2y (x - 2)(x^2 + 8)
There are other methods of factorising (x^3 - 2x^2 + 8x - 16), so use the method which you have been taught in class or the one I used.
Answer:
Step-by-step explanation:
Because you can't do -x+1 so it would be (1,0) and then you have x^2 +3x-4 which is (-5,6)
