Answer:
The required answer is
.
Step-by-step explanation:
The given differential equation is
![\frac{dy}{dx}=(x-y+1)^2](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%28x-y%2B1%29%5E2)
Substitute u=x-y+1 in the above equation.
![\frac{du}{dx}=1-\frac{dy}{dx}](https://tex.z-dn.net/?f=%5Cfrac%7Bdu%7D%7Bdx%7D%3D1-%5Cfrac%7Bdy%7D%7Bdx%7D)
![\frac{dy}{dx}=1-\frac{du}{dx}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D1-%5Cfrac%7Bdu%7D%7Bdx%7D)
![1-\frac{du}{dx}=u^2](https://tex.z-dn.net/?f=1-%5Cfrac%7Bdu%7D%7Bdx%7D%3Du%5E2)
![1-u^2=\frac{du}{dx}](https://tex.z-dn.net/?f=1-u%5E2%3D%5Cfrac%7Bdu%7D%7Bdx%7D)
Using variable separable method, we get
![dx=\frac{du}{1-u^2}](https://tex.z-dn.net/?f=dx%3D%5Cfrac%7Bdu%7D%7B1-u%5E2%7D)
Integrate both the sides.
![\int dx=\int \frac{du}{1-u^2}](https://tex.z-dn.net/?f=%5Cint%20dx%3D%5Cint%20%5Cfrac%7Bdu%7D%7B1-u%5E2%7D)
![[\because \int \frac{dx}{a^2-x^2}=\frac{1}{2a}\n|\frac{a+x}{a-x}|+C]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cint%20%5Cfrac%7Bdx%7D%7Ba%5E2-x%5E2%7D%3D%5Cfrac%7B1%7D%7B2a%7D%5Cn%7C%5Cfrac%7Ba%2Bx%7D%7Ba-x%7D%7C%2BC%5D)
Substitute u=x-y+1 in the above equation.
![x+C=\frac{1}{2}\ln|\frac{1+x-y+1}{1-(x-y+1)}|](https://tex.z-dn.net/?f=x%2BC%3D%5Cfrac%7B1%7D%7B2%7D%5Cln%7C%5Cfrac%7B1%2Bx-y%2B1%7D%7B1-%28x-y%2B1%29%7D%7C)
![x+C=\frac{1}{2}\ln|\frac{2+x-y}{y-x}|](https://tex.z-dn.net/?f=x%2BC%3D%5Cfrac%7B1%7D%7B2%7D%5Cln%7C%5Cfrac%7B2%2Bx-y%7D%7By-x%7D%7C)
Therefore the required answer is
.
Answer:
the correct answer is x = 3x - 5
Answer:
15/33
Step-by-step explanation:
total pieces=33
Pieces eaten=18
Left=33-18
=15
Fraction=15/33
Answer:
what is the question of this?
Answer:
Yes
Step-by-step explanation:
If the garden is 1O by 12 feet then the entire area is 120 feet. If one seed packet needs 40 feet then there will have to be 120 feet to have enough space for all three.
120 = 120, so Jules has enough space.
Stay safe! <3