Answer:
![\therefore y_2(x)=-\frac{e^{-6x}}{8}](https://tex.z-dn.net/?f=%5Ctherefore%20y_2%28x%29%3D-%5Cfrac%7Be%5E%7B-6x%7D%7D%7B8%7D)
The general solution is
![y=c_1e^{2x}-c_2.\frac{e^{-6x}}{8}](https://tex.z-dn.net/?f=y%3Dc_1e%5E%7B2x%7D-c_2.%5Cfrac%7Be%5E%7B-6x%7D%7D%7B8%7D)
Step-by-step explanation:
Given differential equation is
y''-4y'+4y=0
and ![y_1(x)=e^{2x}](https://tex.z-dn.net/?f=y_1%28x%29%3De%5E%7B2x%7D)
To find the
we are applying the following formula,
![y_2(x)=y_1(x)\int \frac{e^{-\int P(x) dx}}{y_1^2(x)} \ dx](https://tex.z-dn.net/?f=y_2%28x%29%3Dy_1%28x%29%5Cint%20%5Cfrac%7Be%5E%7B-%5Cint%20P%28x%29%20dx%7D%7D%7By_1%5E2%28x%29%7D%20%5C%20dx)
The general form of equation is
y''+P(x)y'+Q(x)y=0
Comparing the general form of the differential equation to the given differential equation,
So, P(x)= - 4
![\therefore y_2(x)=e^{2x}\int \frac{e^{-\int 4dx}}{(e^{2x})^2}dx](https://tex.z-dn.net/?f=%5Ctherefore%20y_2%28x%29%3De%5E%7B2x%7D%5Cint%20%5Cfrac%7Be%5E%7B-%5Cint%204dx%7D%7D%7B%28e%5E%7B2x%7D%29%5E2%7Ddx)
![=e^{2x}\int \frac{e^{-4x}}{e^{4x}}dx](https://tex.z-dn.net/?f=%3De%5E%7B2x%7D%5Cint%20%5Cfrac%7Be%5E%7B-4x%7D%7D%7Be%5E%7B4x%7D%7Ddx)
![=e^{2x}\int e^{-4x-4x} \ dx](https://tex.z-dn.net/?f=%3De%5E%7B2x%7D%5Cint%20e%5E%7B-4x-4x%7D%20%5C%20dx)
![=e^{2x}\int e^{-8x} \ dx](https://tex.z-dn.net/?f=%3De%5E%7B2x%7D%5Cint%20e%5E%7B-8x%7D%20%5C%20dx)
![=e^{2x}. \frac{e^{-8x}}{-8}](https://tex.z-dn.net/?f=%3De%5E%7B2x%7D.%20%5Cfrac%7Be%5E%7B-8x%7D%7D%7B-8%7D)
![=-\frac{e^{-6x}}{8}](https://tex.z-dn.net/?f=%3D-%5Cfrac%7Be%5E%7B-6x%7D%7D%7B8%7D)
![\therefore y_2(x)=-\frac{e^{-6x}}{8}](https://tex.z-dn.net/?f=%5Ctherefore%20y_2%28x%29%3D-%5Cfrac%7Be%5E%7B-6x%7D%7D%7B8%7D)
The general solution is
![y=c_1e^{2x}-c_2.\frac{e^{-6x}}{8}](https://tex.z-dn.net/?f=y%3Dc_1e%5E%7B2x%7D-c_2.%5Cfrac%7Be%5E%7B-6x%7D%7D%7B8%7D)
Are there other answers or just those 2
Answer:
Step-by-step explanation:
area of a full circle is A = πr²
so a quarter of a circle area is A = πr²/4
A = 3.142(7²)/4
A = 38.4895 cm² picture answer
Using π = 3.14 results in
A = 3.14(7²)/4
A = 38.465 cm² written question answer
For comparison purposes,
Carrying the precision of π into many more significant digits results in
A = 38.484510006474...cm²
6(x²-4x+4-4)+1=0, 6(x-2)²-24+1=0, 6(x-2)²=23, x-2=±√(23/6), x=2±√(23/6)=2±1.95789, so x=3.95789 or 0.04211 approx. These are the zeroes.
Answer:
I attached the answers :)
Step-by-step explanation:
hope this helps :)
(Its a bit messy becuz i used a mouse to write, sry about that)