Step 1:

The derivative equation is $\"\"$

$\"\"$ Comparing the differential equation form $\"image\"$

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

$\"image\"$

$\"\"$

Put 2 x + 3 y = t

$\"image\"$

Substitute the t value in $\"\"$

dy / dx = - ( t - 1 ) / ( t +2 )

Therefore $\"\"$

$\"\"$

Let us take intigration on each term.

$\"\"$ \ \ \ \ Substitute the t value

$\"\"$

Solution:

$\"\"$