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in Differential equations by (37.0k points)

Solve: (4x – 3y)dx + (2y – 3x)dy = 0.

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Best answer

The given differential equation is 

(4x – 3y)dx + (2y – 3x)dy = 0 

4xdx + 2ydy – 3(xdy + ydx) = 0 

4xdx + 2ydy – 3d(xy) = 0 

Integrating, we get 

2x2 + y2 – 3xy = c 

which is the required solution of the given differential equation.

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