Question

Consider the DE. (4x−y)dx+(6y−x)dy=0 then the DE is Fₓ²

Hencel F(x,y)= thisfore the Ceneral solution of the DE is

Answer 1

To solve the given differential equation (4x−y)dx+(6y−x)dy=0, we can use the method of separate variables. After separating the variables and integrating, we get the general solution of 2x^2 - xy = x^2 - 3y^2 + C.

Step-by-step explanation:

The given differential equation is (4x−y)dx+(6y−x)dy=0. To solve this equation, we can use the method of separate variables.

First, we separate the variables by isolating the x and y terms on different sides of the equation:

(4x−y)dx = (x-6y)dy

Next, we integrate both sides with respect to their respective variables:

∫(4x−y)dx = ∫(x-6y)dy

Integrating, we get:

2x^2 - xy = x^2 - 3y^2 + C

Where C is the constant of integration. This is the general solution to the given differential equation.