( x^2 + y^2 ) dx + x (3x^2 - 5y^2 ) dy = 0
$(x^2 + y^2)\,dx + x(3x^2 - 5y^2)\,dy = 0$
The variables are not separable The equation is not homogeneous
Try:
$\dfrac{dx}{dy} + \dfrac{x(3x^2 - 5y^2)}{x^2 + y^2} = 0$
The equation is not linear.
$N = 3x^3 - 5xy^2$ → $\dfrac{\partial N}{\partial x} = 9x^2 - 5y^2$
The equation is not exact
$\dfrac{\dfrac{\partial M}{\partial y} - \dfrac{\partial N}{\partial x}}{N} = \dfrac{2y - 9x^2 + 5y^2}{3x^3 - 5xy^2}$
The equation does not have an integrating factor that is a function of x alone
$\dfrac{\dfrac{\partial M}{\partial y} - \dfrac{\partial N}{\partial x}}{N} = \dfrac{2y - 9x^2 + 5y^2}{x^2 + y^2}$
The equation does not have an integrating factor that is a function of y alone
Wala pa akong nakitang solution. Kung meron ka na, pease share.
eto po yung answer:
2y^5 - 2x^2 ( y^3) + 3x = 0
Are you sure your equation is correct? And based on your answer key, there should be an initial condition because there is no constant c in your answer.
The equation is wrong it should be y(x^2+y^2)dx+x(3x^2-5y^2)dy=0, when x=2 , y=1
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$(x^2 + y^2)\,dx + x(3x^2 - 5y^2)\,dy = 0$
The variables are not separable
The equation is not homogeneous
Try:
$\dfrac{dx}{dy} + \dfrac{x(3x^2 - 5y^2)}{x^2 + y^2} = 0$
The equation is not linear.
Try:
$N = 3x^3 - 5xy^2$ → $\dfrac{\partial N}{\partial x} = 9x^2 - 5y^2$
The equation is not exact
Try:
$\dfrac{\dfrac{\partial M}{\partial y} - \dfrac{\partial N}{\partial x}}{N} = \dfrac{2y - 9x^2 + 5y^2}{3x^3 - 5xy^2}$
The equation does not have an integrating factor that is a function of x alone
Try:
$\dfrac{\dfrac{\partial M}{\partial y} - \dfrac{\partial N}{\partial x}}{N} = \dfrac{2y - 9x^2 + 5y^2}{x^2 + y^2}$
The equation does not have an integrating factor that is a function of y alone
Wala pa akong nakitang solution. Kung meron ka na, pease share.
eto po yung answer:
2y^5 - 2x^2 ( y^3) + 3x = 0
Are you sure your equation is correct? And based on your answer key, there should be an initial condition because there is no constant c in your answer.
The equation is wrong it should be y(x^2+y^2)dx+x(3x^2-5y^2)dy=0, when x=2 , y=1
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