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!