The solution of differential equation `dy/dx=(4x+6y+5)/(3y+2x+4)` is

Explanation

`dy/dx = (2(2x+3y)+5)/(3y+2x+4)`

let `2x+3y= t`

`2 + 3 dy/dx = dt/dx`

`dy/dx= 1/3(dt/dx- 2)`

`1/3 dy/dx -2/3 = (2t+5)/(t+4)`

`1/3dt/dx = (2t +5)/(t+4) +2/3 => (6t + 15 + 2t + 8)/(3(t+4))`

`1/3 dt/dx = (8t +23)/(3(t+4))`

`int ((t+4)/(8t +23)) dt = int dx`

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