Differential equation problem

  • Thread starter tunabeast
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  • #1
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Homework Statement


[tex]x^2\frac{dy}{dx}=\frac{2sqrt(y)}{x^4}[/tex]

Where y(1)=3


Homework Equations





The Attempt at a Solution


[tex]\int \frac{dy}{2sqrt(y)}=\int \frac{dx}{x^4}[/tex]

[tex]4sqrt(y)=\frac{-1}{3x^3}+c[/tex]

[tex]c=4sqrt(3)+\frac{1}{3}[/tex]

So i end up with

[tex]4sqrt(y)=\frac{-1}{3x^3}+4sqrt(3)+\frac{1}{3} [/tex]

I'v gone wrong somewhere as the solution given does not match, i just can't spot where my mistake is. Thanks in advance for any help
 

Answers and Replies

  • #2
126
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Hello,

How'd you get [tex]\int \frac{dy}{2\sqrt{y}}=\int \frac{dx}{x^4}[/tex]
from

[tex]x^2\frac{dy}{dx}=\frac{2\sqrt{y}}{x^4}[/tex]?

What happened to the [itex]x^2[/itex] term on the left?
 
  • #3
27
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Sorry about that, stupid error. In the initial problem it should be [tex]\frac{2sqrt(y)}{x^2}[/tex]
 
  • #4
Dick
Science Advisor
Homework Helper
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Differentiate 4*sqrt(y). Do you get 1/(2*sqrt(y))?
 

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