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First order differential equation questionby idks16
Tags: differential eqns 
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#1
Jan1513, 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? 


#2
Jan1513, 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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