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
.
The answer to this question is D. 4
Answer:
A = 12.56 m²
General Formulas and Concepts:
<u>Pre-Alg</u>
- Order of Operations: BPEMDAS
<u>Geometry</u>
- Area of a Circle: A = πr²
- d = 2r
Step-by-step explanation:
<u>Step 1: Define</u>
d = 4 m
<u>Step 2: Find </u><em><u>r</u></em>
- Substitute: 4 = 2r
- Isolate <em>r</em>: 2 = r
- Rewrite: r = 2 m
<u>Step 3: Find Area</u>
- Substitute: A = π(2)²
- Substitute: A = (3.14)(2)²
- Evaluate: A = (3.14)(4)
- Multiply: A = 12.56 m²
147.59 is the total amount given to each brother after all purchases were made.