Question

solve: (2x+3y-1) dx+(2x+3y-5) dy=0

Answer 1

Comparing the differential equation  form

a ₁ = - 2 , b ₁ = - 3 , c ₁ = 1,  a₂ = 2 , b ₂ =  3 , c ₂ = - 5.

It is non homogenous equation.

Case (1) :-  b₁ + a ₂ = 0

- 3 + 2 = - 1 ≠ 0

Case (2) :-  a ₁ / a ₂ = b ₁ / b₂

Put 2 x + 3 y = t

Substitute the t value in

dy / dx = - ( t - 1 ) / ( t - 5 )

Therefore  

Let us take intigration on each trem.

Substitute the t value

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