Solve `(4x+3y-4)dx+(3x-7y-3)dy=0`

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#### Solution

Given, `(4x+3y-4)dx+(3x-7y-3)dy=0`

∴ `M=(4x+3y-4) and (3x-7y-3)`

Differentiating M by y and N by x, we get,

`(dM)/dy=3` And `(dN)/dx=3`

∴` (dM)/dy=(dn)/dx`

∴ The given equations are exact.

For solution,

`int M dx=int (4x+3y-4)dx`

`int M dx = 2x^2+3xy-4x`

`int" (Term is N free from x)"=int-7y-3 dy`

= `(-7y^2)/2-3y`

∴ The final solution is,

`2x^2+3xy-4x-(7y^2)/2-3y=c`

`4x^2+6xy-8x-7y^2-6y=c`

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function

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