Where am I missing a constant of integration? I thought the constant of integratoin on one side cancels out with the constant of integration on the other side.
Where am I missing a constant of integration? I thought the constant of integratoin on one side cancels out with the constant of integration on the other side.
What you have is:
This has solution
Or to put it another way, you would have two arbitrary constants doing it your way. The sum and difference of arbitrary constants are both another arbitrary constant. That is the two constants are not equal.
Where am I missing a constant of integration? I thought the constant of integratoin on one side cancels out with the constant of integration on the other side.
In that case; this is an exercise in the use of the fundamental theorem of calculus not in differential equations (so don't try to separate the variables).