# Math Help - bernoulli equation

1. ## bernoulli 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.

2. Originally Posted by markmil2002
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.
Note that $\frac{\,dy}{\,dx}-2y=\frac{4x}{y^{\frac{1}{2}}}\implies \frac{\,dy}{\,dx}-2y=4xy^{-\frac{1}{2}}$,

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

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!

--Chris