Solve the Differential equation

Question

accessdenied · Answer

Can you describe your work up to your answer?  Then we can see if there are any issues and where they are located.

anonymous · Answer

$$15x^2+C$$$$63=15(2)^2+C$$$$3 = C$$

$$15x^2 + 3$$$$5x^3+3x+C$$$$9=5(1)^3+3(1)+C$$$$1 = C$$
$$5x^3+3x+1$$

I'm not 100% sure how to go about solving these, but this is what i got

accessdenied · Answer

I agree with your work here.  :)
In this case, we had the second derivative of our unknown function equal to some function of x.  So we can integrate both sides with respect to x to reduce the derivative order on the left.  Then our initial conditions will let us find those constants of integration by result of indefinite integrals.  The process is repeated until we found f(x) with no constant variables remaining.

anonymous · Answer

So I got it right? :D

accessdenied · Answer

Yes. :)

anonymous · Answer

Sweet not as hard as I thought they were! thanks a lot

accessdenied · Answer

Yep, glad to help!
They only get trickier if you get into the ones where f(x) and f'(x) (and higher orders)  are floating around in the equation, or they just put really weird functions to integrate.  :p