Question

Please help me solve the given differential equation by separation of variables.

(4y+yx^2)dy=(2x+xy^2)dx

Answer 1

\[(4y+yx^2)dy=(2x+xy^2)dx\]

Answer 2

ok this is a fun one :)

Answer 3

first you want to pull out the variables from each parenthesis, \[(4y + yx ^{2})dy = y(4 + x ^{2}) dy \]
and \[(2x + xy ^{2}) dx = x(2 + y ^{2})\]

Answer 4

Forgot the dx on 2nd part

Answer 5

Than the expression becomes \[y(4 + x^{2}) dy = x(2+y^{2}) dx\] divide so that X's are on right and Y's are on left

Answer 6

This gives you: \[\left( \frac{ y }{ 2 + y^{2} } \right) dy = \left( \frac{ x }{ 4+x^{2} } \right) dx\]

Answer 7

oh ok thank you, I believe I can go from here.

should all solutions of separation of variable problems be set equal to y?

Answer 8

Well you want to get the y's with the dy and the x's with the dx

Answer 9

but most cases you are solving for a function that is of the form y(x)

Answer 10

y(x) = expression

Answer 11

right, but I'm talking about the final solution

Answer 12

right ok