# Question #a16d8

##### 1 Answer

The solution is

#### Explanation:

Integrate by parts on the right-hand side. Let

The integration by parts formula states that

Therefore:

#int(x - 8)x^-1 = (x- 8)ln|x| - int(ln|x|)#

We will now need to reintegrate using integration by parts.

We let

#" "= xln|x| - x#

#" "=x(ln|x| - 1) + C#

So, the complete integration, after integrating both sides, will be:

#y = (x -8)ln|x| - (x(ln|x| -1)) + C#

#y= (x- 8)ln|x| - xln|x| + x + C#

#y = xln|x| - 8ln|x| - xln|x| + x + C#

#y= x - 8ln|x| + C#

We want the equation that passes through

#2 = (1- 8)ln|1| - 1(ln|1|) + 1 + C#

#2 = -7(0) - 1(0) + 1 + C#

#2 - 1 = C#

#C = 1#

The solution to the differential equation is therefore

Hopefully this helps!