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How to solve this differential equation

dy/dx = (x^2+y^2)/y using the substitution y = z^1/2.
Please can someone help me solve this equation, I get:

d/dx(z^1/2) = (x^2 - z)/z^1/2
(x^2 - z)/z^1/2 = (1/2z^1/2)dz/dx
dz/dx = 2(x^2-z)
and I don't know how to separate this, do I need to find an integrating factor?
Any help would be much appreciated, thanks :biggrin:
(edited 8 years ago)
Original post by Jingram123
dy/dx = (x^2+y^2)/y using the substitution y = z^1/2.
Please can someone help me solve this equation, I get:

d/dx(z^1/2) = (x^2 - z)/z^1/2
(x^2 - z)/z^1/2 = (1/2z^1/2)dz/dx
dz/dx = 1(x^2-z)
and I don't know how to separate this, do I need to find an integrating factor?
Any help would be much appreciated, thanks :biggrin:


Don't forget the 1/2 from your second line to your third line :smile:

I suspect that an integrating factor is required.
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Jingram123
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oh yeah, sorry that was a typo, thanks, but the working is correct other than that, right?
Original post by Jingram123
oh yeah, sorry that was a typo, thanks, but the working is correct other than that, right?


Yes, it should be okay, and you can find the integrating factor.
Are you struggling?

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