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 
.
![\boxed{pd\sqrt[4]{48p^3d}}](https://tex.z-dn.net/?f=%5Cboxed%7Bpd%5Csqrt%5B4%5D%7B48p%5E3d%7D%7D)
<h2>
Explanation:</h2>
Here we have the following expression:
![\sqrt[4]{48p^7d^5}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B48p%5E7d%5E5%7D)
So we need to simplify it:
![\sqrt[4]{48p^7d^5} \\ \\ \\ We \ can \ write: \\ \\ p^7=p^4\cdot p^3 \\ \\ d^5=d^4\cdot d \\ \\ \\ So: \\ \\ \sqrt[4]{48p^4\cdot p^3\cdot d^4\cdot d} \\ \\ \\ By \ property: \\ \\ \sqrt[n]{x^n}=x \\ \\ \\ Finally: \\ \\ \boxed{pd\sqrt[4]{48p^3d}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B48p%5E7d%5E5%7D%20%5C%5C%20%5C%5C%20%5C%5C%20We%20%5C%20can%20%5C%20write%3A%20%5C%5C%20%5C%5C%20p%5E7%3Dp%5E4%5Ccdot%20p%5E3%20%5C%5C%20%5C%5C%20d%5E5%3Dd%5E4%5Ccdot%20d%20%5C%5C%20%5C%5C%20%5C%5C%20So%3A%20%5C%5C%20%5C%5C%20%5Csqrt%5B4%5D%7B48p%5E4%5Ccdot%20p%5E3%5Ccdot%20d%5E4%5Ccdot%20d%7D%20%5C%5C%20%5C%5C%20%5C%5C%20By%20%5C%20property%3A%20%5C%5C%20%5C%5C%20%5Csqrt%5Bn%5D%7Bx%5En%7D%3Dx%20%5C%5C%20%5C%5C%20%5C%5C%20Finally%3A%20%5C%5C%20%5C%5C%20%5Cboxed%7Bpd%5Csqrt%5B4%5D%7B48p%5E3d%7D%7D)
<h2>Learn more:</h2>
Mathematical expressions: brainly.com/question/14200575#
#LearnWithBrainly
The numbers are 59 and 61
2 feet 7 inches.
5 feet - 2 feet is 3 feet
3 inches - 8 inches is - 5 inches.
just take the 5 inches from 3 feet to get 2 feet 7 inches.
Answer:
∠A=65º
Step-by-step explanation:
- A angle of a line is 180º, so we can say that angle ABC=(180-6x)º
- The interior angkes of a triangle is 180º, so (x+40)º+(3x+10)º+(180-6x)º=180º
- Remove parenthesis, x+40+3x+10+180-6x=180
- Combine like terms, -2x+230=180
- Subtract 180, -2x=-50
- Divide by -2, so x=25
Now:
- ∠CAB=(25+40)º=65º
- ∠ABC=[180-6(25)]º=30º
- ∠BCA=[3(25)+10]=85º
