Differentiate the given solution:

Substitute
and
into the ODE:

and it's easy to see the left side indeed reduces to 0.
Answer:
x = 26
Step-by-step explanation:
Given
(x - 2) =
(x + 4) + 2
Multiply through by 15 to clear the fractions
5(x - 2) =3(x + 4) + 30 ← distribute and simplify both sides
5x - 10 = 3x + 12 + 30, that is
5x - 10 = 3x + 42 ( subtract 3x from both sides )
2x - 10 = 42 ( add 10 to both sides )
2x = 52 ( divide both sides by 2 )
x = 26
The correct answer to this problem would be -3. Based on the points you've provided on the graph, -3 would be the correct common difference. :)