Answer:
x=2
Step-by-step explanation:
1/2x+3=5/2x-1
1/2-5/2x=-1-3
-4/2x=-4
-2x=-4
x=-4/-2
x=2
<span>Mrs
Marks has 3/5 pound of cheese.
She’s using 1/32 pound of cheese in every sandwhich.
Now, how many sandwhiches can she make with her current pound of cheese
=> ¾ / 1/32
Find the Least common multiple of both denominator since they are not the same.
=> the LCM is 32
=> ¾ = 24/32
=> 1/32
=. 24/32 X 1/32
=> 24, Mrs. Mark can make 24 sandwhiches out of her ¾ cheese. </span>
Let
![y=C_1x+C_2x^3=C_1y_1+C_2y_2](https://tex.z-dn.net/?f=y%3DC_1x%2BC_2x%5E3%3DC_1y_1%2BC_2y_2)
. Then
![y_1](https://tex.z-dn.net/?f=y_1)
and
![y_2](https://tex.z-dn.net/?f=y_2)
are two fundamental, linearly independent solution that satisfy
![f(x,y_1,{y_1}',{y_1}'')=0](https://tex.z-dn.net/?f=f%28x%2Cy_1%2C%7By_1%7D%27%2C%7By_1%7D%27%27%29%3D0)
![f(x,y_2,{y_2}',{y_2}'')=0](https://tex.z-dn.net/?f=f%28x%2Cy_2%2C%7By_2%7D%27%2C%7By_2%7D%27%27%29%3D0)
Note that
![{y_1}'=1](https://tex.z-dn.net/?f=%7By_1%7D%27%3D1)
, so that
![x{y_1}'-y_1=0](https://tex.z-dn.net/?f=x%7By_1%7D%27-y_1%3D0)
. Adding
![y''](https://tex.z-dn.net/?f=y%27%27)
doesn't change this, since
![{y_1}''=0](https://tex.z-dn.net/?f=%7By_1%7D%27%27%3D0)
.
So if we suppose
![f(x,y,y',y'')=y''+xy'-y=0](https://tex.z-dn.net/?f=f%28x%2Cy%2Cy%27%2Cy%27%27%29%3Dy%27%27%2Bxy%27-y%3D0)
then substituting
![y=y_2](https://tex.z-dn.net/?f=y%3Dy_2)
would give
![6x+x(3x^2)-x^3=6x+2x^3\neq0](https://tex.z-dn.net/?f=6x%2Bx%283x%5E2%29-x%5E3%3D6x%2B2x%5E3%5Cneq0)
To make sure everything cancels out, multiply the second degree term by
![-\dfrac{x^2}3](https://tex.z-dn.net/?f=-%5Cdfrac%7Bx%5E2%7D3)
, so that
![f(x,y,y',y'')=-\dfrac{x^2}3y''+xy'-y](https://tex.z-dn.net/?f=f%28x%2Cy%2Cy%27%2Cy%27%27%29%3D-%5Cdfrac%7Bx%5E2%7D3y%27%27%2Bxy%27-y)
Then if
![y=y_1+y_2](https://tex.z-dn.net/?f=y%3Dy_1%2By_2)
, we get
![-\dfrac{x^2}3(0+6x)+x(1+3x^2)-(x+x^3)=-2x^3+x+3x^3-x-x^3=0](https://tex.z-dn.net/?f=-%5Cdfrac%7Bx%5E2%7D3%280%2B6x%29%2Bx%281%2B3x%5E2%29-%28x%2Bx%5E3%29%3D-2x%5E3%2Bx%2B3x%5E3-x-x%5E3%3D0)
as desired. So one possible ODE would be
![-\dfrac{x^2}3y''+xy'-y=0\iff x^2y''-3xy'+3y=0](https://tex.z-dn.net/?f=-%5Cdfrac%7Bx%5E2%7D3y%27%27%2Bxy%27-y%3D0%5Ciff%20x%5E2y%27%27-3xy%27%2B3y%3D0)
(See "Euler-Cauchy equation" for more info)
There are many different kinds of quadrilaterals, but all have several things in common: all of them have four sides, are coplanar, have two diagonals, and the sum of their four interior angles equals 360 degrees. This is how they are alike, but what makes them different?
<span>
</span>