
Differential equations
I'm after some help with these two equations.
My problem is factorising with equations like this, I can never tell when I'm supposed to do it!! I have the answers to these questions I just need explicit help, basically a walk through of these examples, if anyone can help I'd much appreciate it,
Thanks
ydy/dx+7x^2+7x+5=0
which satisfies y(0)=4
The Answer is:
sqrt(16(14/3x^3 + 7x^2+10x))
and my other problem is,
dy/dx = 1+y^2/7+9x
which satisfies y(1) = 0
tan(1/9ln(7+9x/16))
With regards to the last answer, how does PI sometimes come out of this answer?
PS how do you write with math symbols, it looks a bit messy....

Both of them are separable.
(See my signature for LaTeX typesetting.)

A separable differential equation is an equation that can be expressed in this form:
Like,
You can solve them by separating the functions and differentials to the sides and integrating.
For example,
Move to the right and to the left.
Now you can integrate both sides.
We can use only C instead of two integration constants.

Your first question is,
,
Start by separating.
Now we can integrate both sides.


Try for both of them.





As is always positive, this equation doesn't have a root.
So we found that our function is because this is the only valid function that makes . And we found that .
Hence, the function we are looking for is:

Now try to solve the second equation (Wink)