Question

Solve the differential equation
dy/dx=x+y+4/x-y-6

Answer 1

Answer:

I don't know..... jhhj

Answer 2

The answer is $y = \frac{x^{2}}{2}+4\ln x -6x$

Step-by-step explanation:

The differential equation,

$\Rightarrow \frac{\mathrm{d} y}{\mathrm{d} x}= x + y+ \frac{4}{x}-y-6$

$\Rightarrow \frac{\mathrm{d} y}{\mathrm{d} x}= x + \frac{4}{x}-6$

$\Rightarrow {\mathrm{d} y} = \left ( x + \frac{4}{x}-6 \right )\times{\mathrm{d} x}$

Now integrating on both side,

$\Rightarrow \int {\mathrm{d} y} = \int \left ( x + \frac{4}{x}-6 \right )\times{\mathrm{d} x}$

$\Rightarrow  y = \frac{x^{2}}{2}+4\ln x -6x$