1.

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

Answer» `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`
`1/8 int((8t +32)/(8t+32)) dt = x+ c`
`= 1/8 int((8t + 23 +9)/(8t +23))dt= x+ c`
`= 1/8 int dt + int 9/(8t+23)dt= x+ c `
`1/8[ t] + 9/8 int (du)/u `
`1/8[2x+3y + 9/8ln(8t+23)]= x+c`
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