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differential equations need help?
I am having some trouble figuring out some of these equations. I can't seem to fully separate them apart and always run into problems. Can you please explain how to answer these? C &D are initial value problems used to find C. In the first two, just denote that integration constant as C.
A) x dv/dx = (5-9v^2)/(3v)
B) (7x^5+x^5y^2)dx + e^(x^(6))y dy = 0
C) dy/dx = (1+y^2)tan(x) ------Y(0)=1
D) dy/dx = (3x^2+8x+2)/(2y+2) ----Y(0)=-2
Untitled:
For A, I get something to the nature of +/- Sqrt ((5-e^(-6Cln(abs(x)))/9) And wolfram is spitting out something completely different, and I'm not sure why.
2 Answers
- RapidfireLv 710 years agoFavorite Answer
Please post one question at a time, makes it more manageable to answer.
- untitledLv 410 years ago
A) Just put the x's together on one side (where dx is) and the v's on the other side (where dv is):
(3v)/(5-9v^2) dv = 1/x dx.
Then you integrate both sides.
B) First factor the x^5 out of the parenthesis. Then divide both sides of the equation by (7+y^2) and then by e^(x^6). And bring the y's together in the other side.
You will get -(x^5)/e^(x^6) dx = y/(7+y^2) dy
The idea is to find a function of only y times dy on one side and a function of only x times dx.
The position of the dx's and dy's tells you on which side to bring the x's and y's, because if they were on the other side, then dx (or dy) would turn into 1/dx (or 1/dy) which is useless.
