solve for the de (2x + 3y - 1)dx + (2x + 3y + 2)dy = 0

Answer 1

Step 1:

The derivative equation is

Comparing the differential equation form

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

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 +2 )

Therefore

Let us take integration on each term.

Substitute the t value

Solution: