Suppose 
is another solution. Then
Substituting these derivatives into the ODE gives
Let 
, so that
Then the ODE becomes
and we can condense the left hand side as a derivative of a product,
![\dfrac{\mathrm d}{\mathrm dx}[x^5u]=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Bx%5E5u%5D%3D0)
Integrate both sides with respect to 
:
![\displaystyle\int\frac{\mathrm d}{\mathrm dx}[x^5u]\,\mathrm dx=C](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Bx%5E5u%5D%5C%2C%5Cmathrm%20dx%3DC)
Solve for 
:
Solve for 
:
So another linearly independent solution is 
.
X + 4y = 9 Convert to slope / intercept form:-
y = (-1/4)x + 9/4
so the line perpendicular to this will have a slope -1 /(-1/4) = 4
so our equation will be y - y1 = 4(x - x1) where x1y1 is a point on the line.
x1 = 8 and y1 = -3:-
y - -3 = 4(x - 8)
y = 4x - 35
-4x + y = -35 is the answer
Answer:
1.75 hours and 2 Hours
Step-by-step explanation:
Answer:
x=1/14 and y=1/12
Step-by-step explanation:
7x+5y+12+7x+7y=14
⇒14x+12y=2
and set x and y in 0
then you will have 14*(1/7)=2 and 12*(1*6)=2
and you want somthing that makes x + y =2
so you sett 14*x=1 and 12*y=1
that is if i did noy misunderstanding the question
1) given function
y = - 2 ^ ( -x + 2) + 1
2) domain: domain is the set of the x-values for which the function is defined.
The exponential function is defined for all the real numbers, so the domain of the given function is all the real numbers.
3) x-intercept => y = 0
=> y = - 2 ^ ( -x + 2) + 1 = 0 => 2^ ( -x + 2) = 1
=> - x + 2 = 0 => x = 2
The x-intercept is x = 0
4) y-intercept => x = 0
=> y = - 2 ^ ( -x + 2) + 1= - 2 ^ ( 0 + 2) 1 = - (2)^(2) + 1 =- 4 + 1 = - 3
=> The y-intercept is - 3
5) limit when x -> negative infinite
Lim f(x) when x -> ∞ = - ∞
6) limit when x -> infinite
Lim f(x) when x - > infinite = 1
=> asymptote = y = 1
7) range is the set of values of the fucntion: y
Given that the function is strictly decreasing from -∞ to ∞, the range is from - ∞ to less than 1
Range (-∞,1)
