Question

Determine whether the equation is exact. If it is exact, find the solution.

\((3x^2-2xy+2)+(6y^2-x^2+3)y\prime=0\)

Answer 1

basically what you want to do is combine like terms first then you solve from there

Answer 2

You take differential equations?

Answer 3

Did you check for exactness yes?
\[\Large M_y=N_x \]

Answer 4

I haven't worked on this in a while, how exactly would I do that?

Answer 5

Consider the differential equation in it's original form:
\[\Large M(x,y)+N(x,y)y'=0 \]
for this differential equation to be exact you must first compute the partial differentials:
\[\Large M_y=N_x \]
if they are exact you can continue from there by assuming that there exists a function with your desired values.

Answer 6

That would be any function of the following form:
\[\Large F_x+F_yy'=0\] (multivariable chainrule)

Answer 7

y'=dy/dx
write the equation in the formM dx+Ndy=0
then see if