I was wondering if anyone can help me in finding a general solution to this:
I've tried using the integrating factor method but I must be getting it wrong or else it's the wrong method to use because the answer is weird...
One way that was suggested was separation of variables.
This is how you would do it with the integrating factor:
Let
Thus, the integrating factor
Now, when you multiply the equation through by , the left side always becomes the derivative of the product between the dependent variable (in this case, ), and the integrating factor.
So we see that the equation now becomes
Integrate both sides and you get
Now multiply both sides by to get the solution
My solution and Showcase_22's are almost the same. However, he made a tiny mistake:
When you integrate, you get
His solution in the end would then be
Note that , another constant.
So we would then get the solution
They now match.
I hope this makes sense!
--Chris