Solve these first order ODEs

• August 15th 2013, 01:59 AM
99.95
Solve these first order ODEs
I am doing these questions from the kreyszig textbook: http://i.imgur.com/atP9Oah.jpg

For Q2, I did:

y^3*y' + x^3 =0

y^3 dy = -x^3 dx

taking the integral of both sides

y^4/4 = -x^4/4 + c
y^4 = -x^4 + c

Then I raised everything to 1/4 power.
leaving us with y = +- (c-x^4)^1/4

However, the wolfram also included an i and -i in front.
Why is that?

Additionally: I have no idea how to do Question 3. Any help would be appreciated.
• August 15th 2013, 04:51 AM
BobP
Re: Solve these first order ODEs
I've no idea about the Wolfram, but for Q3 separate the variables and then use the trig identity $\cos^{2}A=\frac{1}{2}(1+\cos2A).$
• August 15th 2013, 07:52 AM
topsquark
Re: Solve these first order ODEs
Quote:

Originally Posted by 99.95
y^4/4 = -x^4/4 + c
y^4 = -x^4 + c

Note that the four fourth roots of 1 are 1, -1, i, -i.

-Dan