Find y in terms of x if dy/dx=x^6y^-5 and y(0)=6
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Find y in terms of x if dy/dx=x^6y^-5 and y(0)=6

[From: ] [author: ] [Date: 11-08-31] [Hit: ]
When x=0, y=6 so the constant is 6^5, thats 7776.(1/6)y^6 = (1/7)x^7 + 7776.If you prefer,I hope this helps.......
Any help can't seem to get it

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dy/dx = x^6y^-5
Separate the variables.
y^5dy = x^6dx
Integrate.
(1/6)y^6 = (1/7)x^7 + constant
When x=0, y=6 so the constant is 6^5, that's 7776.
(1/6)y^6 = (1/7)x^7 + 7776.
If you prefer, multiply by 42:
7y^6 = 6x^7 + 326592
or
y = { (6x^7+326592)/7 } ^ (1/6)

I hope this helps.

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dy/dx=x^6y^-5
^
Here
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