Thread: Use integral calculus to solve differential equation problems

Please help me to answer this, thank you!

Find the equation of the curve that satisfies the differential equation f"(x) = 6x - 12 and which passes through the points (0, -8) and (1, -1).

Originally Posted by LilDragonfly

Please help me to answer this, thank you!

Find the equation of the curve that satisfies the differential equation f"(x) = 6x - 12 and which passes through the points (0, -8) and (1, -1).

Sooooo:


Thus b = -8.


gives:

or


-Dan

I do not know if you understood what topsquak said, but when you have,

It means if you integrate both sides you have,
with some constant ,
the reason to why f''(x) becomes f'(x) is because when you integrate a derivative of a function you get back the function (definition of integral). So when you have f''(x) integrating once would yield f'(x) so you need one more time:

Then use topsqaurk post to complete the problem.