# Solve ( 4 X + 3 Y − 4 ) D X + ( 3 X − 7 Y − 3 ) D Y = 0 - Applied Mathematics 2

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

#### 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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