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# How to solve this differential equation watch

1. 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
2. (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
Don't forget the 1/2 from your second line to your third line

I suspect that an integrating factor is required.
3. oh yeah, sorry that was a typo, thanks, but the working is correct other than that, right?
4. (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.
5. Are you struggling?

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