dy/dx - 2y = (4x)/(y^1/2)

I assumed that u = y^1/2 would be the proper substitution, but it didn't seem like things were going in the right direction.

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- Sep 10th 2008, 09:45 AMmarkmil2002bernoulli equation
dy/dx - 2y = (4x)/(y^1/2)

I assumed that u = y^1/2 would be the proper substitution, but it didn't seem like things were going in the right direction. - Sep 10th 2008, 09:52 AMChris L T521
Note that $\displaystyle \frac{\,dy}{\,dx}-2y=\frac{4x}{y^{\frac{1}{2}}}\implies \frac{\,dy}{\,dx}-2y=4xy^{-\frac{1}{2}}$,

The substitution is of the form $\displaystyle z=y^{1-n}$, so we see in this case, the proper substitution would be $\displaystyle z=y^{\frac{3}{2}}$

Try to take it from here. This should lead you to the desired result.

See here for an example on how to solve a Bernoulli equation (see post #3)

I hope this helps! (Sun)

--Chris