The ODE is linear:
![y'=x^4-\dfrac yx](https://tex.z-dn.net/?f=y%27%3Dx%5E4-%5Cdfrac%20yx)
![y'+\dfrac yx=x^4](https://tex.z-dn.net/?f=y%27%2B%5Cdfrac%20yx%3Dx%5E4)
Multiplying both sides by
gives
![xy'+y=x^5](https://tex.z-dn.net/?f=xy%27%2By%3Dx%5E5)
Notice that the left side can be condensed as the derivative of a product:
![(xy)'=x^5](https://tex.z-dn.net/?f=%28xy%29%27%3Dx%5E5)
Integrating both sides with respect to
yields
![xy=\dfrac{x^6}6+C](https://tex.z-dn.net/?f=xy%3D%5Cdfrac%7Bx%5E6%7D6%2BC)
![\implies y(x)=\dfrac{x^5}6+\dfrac Cx](https://tex.z-dn.net/?f=%5Cimplies%20y%28x%29%3D%5Cdfrac%7Bx%5E5%7D6%2B%5Cdfrac%20Cx)
Since
,
![1=\dfrac16+C\implies C=\dfrac56](https://tex.z-dn.net/?f=1%3D%5Cdfrac16%2BC%5Cimplies%20C%3D%5Cdfrac56)
so that
![\boxed{y(x)=\dfrac{x^5}6+\dfrac5{6x}}](https://tex.z-dn.net/?f=%5Cboxed%7By%28x%29%3D%5Cdfrac%7Bx%5E5%7D6%2B%5Cdfrac5%7B6x%7D%7D)
Answer:
57 inches
Step-by-step explanation:
It rained 5*6.5+7*3.5=32.5+34.5=57 inches in the past 12 days
Answer:
216
Step-by-step explanation:
LxWxH fill it in 3x6x12=216