# bernoulli equation

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• February 5th 2009, 06:04 PM
crafty
bernoulli equation
xz(dz/dx) = x^2 + 3z^2 with z(1) = 1 ,,,,,,,,,, i have not learned bernoulli's equation and was given this question, although i have read about it on wikipedia, that was not enough can someone give me a step by step explanation of this solution? i do know that i have to perform some sort of substitution but what is that and is there a systematic method to figure out that substitution???? ,,,,,,,,,,,,,,, also my pathetic attempt at this question gave me the answer as ,,,,,,,,,,,,,,, (dy/dx)yx = (x^2)(y^2) + 3 ,,,,,,,,,,,,,,,, i have yet to find the initial value
• February 5th 2009, 06:19 PM
crafty
can't anyone solve this ??????
• February 6th 2009, 07:44 AM
Krizalid
There's no Bernoulli ODE there, it's just a homogeneous ODE, since $xz\,\frac{dz}{dx}={{x}^{2}}+3{{z}^{2}}\implies \frac{dz}{dx}=\frac{x}{z}+\frac{3z}{x}.$

Put $z=yx,$ or having the initial form of your ODE put $y=z^2.$