It is Seperation of Variable, Homogeneous Equation, Exact Equation or Linear Equation?
Question
$\displaystyle (x^3 + y^3) dx + y^2(3x + ky) dy = 0 $ ; $\displaystyle k $ is a constant
Answer
$\displaystyle ky^4 + 4xy^3 + x^4 = c $
It is Seperation of Variable, Homogeneous Equation, Exact Equation or Linear Equation?
Question
$\displaystyle (x^3 + y^3) dx + y^2(3x + ky) dy = 0 $ ; $\displaystyle k $ is a constant
Answer
$\displaystyle ky^4 + 4xy^3 + x^4 = c $
Is this correct? correct if I am wrong.
I used the exact method.
Question
$\displaystyle (x^3 + y^3) dx + y^2(3x + ky) dy = 0 $
Answer
$\displaystyle ky^4 + 4xy^3 + x^4 = c $
Solution:
$\displaystyle (x^3 + y^3) dx + (3xy^2 + ky^3) dy = 0 $
$\displaystyle M = (x^3 + y^3) $
$\displaystyle N = (3xy^2 + ky^3) $
$\displaystyle \frac {\partial M}{\partial y} = 3y^2 $
$\displaystyle \frac {\partial N}{\partial x} = 3y^2 $
$\displaystyle \frac {x^4}{4} + xy^3 + \frac {ky^4}{4} = c $
$\displaystyle ky^4 + 4xy^3 + x^4 = c $
thanks mr fantastic.