DIIFERENTIAL EQUATION: $(x^2 + y^2) dx + x (3x^2 - 5y^2) dy = 0$ Submitted by Sydney Sales on Sat, 07/16/2016 - 16:45 ( x^2 + y^2 ) dx + x (3x^2 - 5y^2 ) dy = 0 Tags Differential Equation, DE Log in to post comments $(x^2 + y^2)\,dx + x(3x^2 - Jhun Vert Sun, 07/17/2016 - 12:57 $(x^2 + y^2)\,dx + x(3x^2 - 5y^2)\,dy = 0$ The variables are not separable The equation is not homogeneous Try: $\dfrac{dy}{dx} + \dfrac{x^2 + y^2}{x(3x^2 - 5y^2)} = 0$ $\dfrac{dx}{dy} + \dfrac{x(3x^2 - 5y^2)}{x^2 + y^2} = 0$ The equation is not linear. Try: $M = x^2 + y^2$ → $\dfrac{\partial M}{\partial y} = 2y$ $N = 3x^3 - 5xy^2$ → $\dfrac{\partial N}{\partial x} = 9x^2 - 5y^2$ The equation is not exact Try: $\dfrac{\dfrac{\partial M}{\partial y} - \dfrac{\partial N}{\partial x}}{N} = \dfrac{2y - (9x^2 - 5y^2)}{3x^3 - 5xy^2}$ $\dfrac{\dfrac{\partial M}{\partial y} - \dfrac{\partial N}{\partial x}}{N} = \dfrac{2y - 9x^2 + 5y^2}{3x^3 - 5xy^2}$ The equation does not have an integrating factor that is a function of x alone Try: $\dfrac{\dfrac{\partial M}{\partial y} - \dfrac{\partial N}{\partial x}}{M} = \dfrac{2y - (9x^2 - 5y^2)}{x^2 + y^2}$ $\dfrac{\dfrac{\partial M}{\partial y} - \dfrac{\partial N}{\partial x}}{N} = \dfrac{2y - 9x^2 + 5y^2}{x^2 + y^2}$ 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. Log in to post comments eto po yung answer: Sydney Sales Sun, 07/17/2016 - 22:53 In reply to $(x^2 + y^2)\,dx + x(3x^2 - by Jhun Verteto po yung answer: 2y^5 - 2x^2 ( y^3) + 3x = 0 Log in to post comments Are you sure your equation is Jhun Vert Mon, 07/18/2016 - 01:26 In reply to $(x^2 + y^2)\,dx + x(3x^2 - by Jhun VertAre 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. Log in to post comments The equation is wrong it Helpme Sat, 08/24/2019 - 11:23 In reply to Are you sure your equation is by Jhun VertThe equation is wrong it should be y(x^2+y^2)dx+x(3x^2-5y^2)dy=0, when x=2 , y=1 Log in to post comments
$(x^2 + y^2)\,dx + x(3x^2 - Jhun Vert Sun, 07/17/2016 - 12:57 $(x^2 + y^2)\,dx + x(3x^2 - 5y^2)\,dy = 0$ The variables are not separable The equation is not homogeneous Try: $\dfrac{dy}{dx} + \dfrac{x^2 + y^2}{x(3x^2 - 5y^2)} = 0$ $\dfrac{dx}{dy} + \dfrac{x(3x^2 - 5y^2)}{x^2 + y^2} = 0$ The equation is not linear. Try: $M = x^2 + y^2$ → $\dfrac{\partial M}{\partial y} = 2y$ $N = 3x^3 - 5xy^2$ → $\dfrac{\partial N}{\partial x} = 9x^2 - 5y^2$ The equation is not exact Try: $\dfrac{\dfrac{\partial M}{\partial y} - \dfrac{\partial N}{\partial x}}{N} = \dfrac{2y - (9x^2 - 5y^2)}{3x^3 - 5xy^2}$ $\dfrac{\dfrac{\partial M}{\partial y} - \dfrac{\partial N}{\partial x}}{N} = \dfrac{2y - 9x^2 + 5y^2}{3x^3 - 5xy^2}$ The equation does not have an integrating factor that is a function of x alone Try: $\dfrac{\dfrac{\partial M}{\partial y} - \dfrac{\partial N}{\partial x}}{M} = \dfrac{2y - (9x^2 - 5y^2)}{x^2 + y^2}$ $\dfrac{\dfrac{\partial M}{\partial y} - \dfrac{\partial N}{\partial x}}{N} = \dfrac{2y - 9x^2 + 5y^2}{x^2 + y^2}$ 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. Log in to post comments
eto po yung answer: Sydney Sales Sun, 07/17/2016 - 22:53 In reply to $(x^2 + y^2)\,dx + x(3x^2 - by Jhun Verteto po yung answer: 2y^5 - 2x^2 ( y^3) + 3x = 0 Log in to post comments
Are you sure your equation is Jhun Vert Mon, 07/18/2016 - 01:26 In reply to $(x^2 + y^2)\,dx + x(3x^2 - by Jhun VertAre 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. Log in to post comments
The equation is wrong it Helpme Sat, 08/24/2019 - 11:23 In reply to Are you sure your equation is by Jhun VertThe equation is wrong it should be y(x^2+y^2)dx+x(3x^2-5y^2)dy=0, when x=2 , y=1 Log in to post comments
$(x^2 + y^2)\,dx + x(3x^2 -
$(x^2 + y^2)\,dx + x(3x^2 - 5y^2)\,dy = 0$
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:
In reply to $(x^2 + y^2)\,dx + x(3x^2 - by Jhun Vert
eto po yung answer:
2y^5 - 2x^2 ( y^3) + 3x = 0
Are you sure your equation is
In reply to $(x^2 + y^2)\,dx + x(3x^2 - by Jhun Vert
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
In reply to Are you sure your equation is by Jhun Vert
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