first order differential equation question


by idks16
Tags: differential eqns
idks16
idks16 is offline
#1
Jan15-13, 09:09 AM
P: 1
The problem is : dy/dx=(x(x^2+1))/4y^3 when y(0)=-1/√2
This is my work so far:
∫4y^3dy=∫x(x^2+1)dx
(y^4)/2=((x^2+1)^2)/2+c
The answer from the textbook is y=-(√(x^2+2)/2)
As you can see, my work will never equal the textbook answer when you put it in the y= stuff form. What did I do wrong?
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grep6
grep6 is offline
#2
Jan15-13, 02:50 PM
P: 5
I got a slightly different answer than what you posted from the text

[itex] y(x) = -\sqrt{\frac{1}{2}(x^2+1)}[/itex]

and mathematica agrees with me, so perhaps a typo?

Anyway, it looks like your on the right track, although go back through the integration, I think you may be off by a factor.
Then apply the boundary condition to find the integration constant.
And simplify the algebra down to the answer.
Also be conscience of taking roots,
[itex] y(x) = (stuff)^{1/4}[/itex]
good luck


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