Find the solution of differential equation dy/dx = x+y+1/2x+2y+3

Question

Find the solution of differential equation

\(\frac{dy}{dx}\) = \(\frac{x+y+1}{2x+2y+3}\)

Answer 1

Given differential equation is

 \(\frac{dy}{dx}\) = \(\frac{x+y+1}{2x+2y+3}\)

where C is an integrating constant,

6v + log (3v + 4) = 9x + 4 (where C₁ = 9C)

or 6(x + y) + log(3x + 3y + 4) = 9x + 4

(Putting the value of v)

or 6y - 3x + log (3x + 3y + 4) = C₁

which is the required solution.