Question

Solve the DE y(2x² - xy + y²)dx - x²(2x - y)dy = 0​

Answer 1

Answer:

xy²(xy) = C

Step-by-step explanation:

y(2x² - xy + y²)dx - x²(2x - y)dy = 0

==> y(y² + 2xy) = 2y + 2x

x(2x² + 3xy) = 2x + 3y

x(2x + y) vx(x,y) - y( 2x + y) uv(x,y) = )-2x + y) v(x,y)

dx/x(2x + 3y) = dy/-y(2x + y) = du/-u(2x + y)

du/dx = u(2x + y)/x(2x + 3y)

du/dy = u/y

F(x,y) = x²y² + xy³

x²y² + xy³ = C

xy²(xy) = C

Answer 2

y(2x² - xy + y²)dx - x²(2x - y)dy = 0