Answer :
- y = (1/6)*In(x - 7)/6 + C
Explanation :
multiply both sides by dx
- (dy/dx)dx = (1/(6x -42))*dx
- dy = (1/(6x -42))*dx
now, integrate both sides of the equation
to integrate the RHS,use u- substitution such that u = 6x -42 making du = 6*dx or dx = du/6 .
substituting the value of dx in the above integral ,
- y = ∫(1/u)(1/6) du
- y = 1/6 ∫(/u) du
- y = (1/6) *Inlul + C
- y = (1/6)*Inl(6x - 42)| + C
or
- y = (1/6)*In(x - 7)/6 + C
