Abernoulli differential equation is one of the form dxdy+p(x)y=q(x)yn observe that, if n=0 or 1, the bernoulli equation is linear. for other values of n, the substitution u=y1−n transforms the bernoulli equation into the linear equation dxdu+(1−n)p(x)u=(1−n)q(x) use an appropriate substitution to solve the equation xy+y=4xy2

It's unclear whether the ODE is

or

If the first case, then divide through both sides by to get

then substitute , so that . Then

If the second, then dividing through by gives

The same substitution as before gives

48 / 6 = x

in this case, x will equal the amount of money in each card!

x therefore will be 8.

trent had $8 in each birthday card.