# Math Help - dif equations

1. ## dif equations

Hi all

which method do i use to solve this:

2. Originally Posted by moolimanj
Hi all

which method do i use to solve this:
Integrating factor method.

But I'd first re-arrange into: $\frac{dy}{dx} + \frac{2}{x} \, y = \frac{5}{x^3}$.

Hint: The integrating factor is $e^{\int \frac{2}{x} \, dx} = e^{2 \ln x} = e^{\ln x^2} = x^2$.

3. sorry to butt in..but I want to understand differential equations better, if you use the integrating factor do you multiply by all the terms? how would you proceed from here?

4. Originally Posted by dankelly07
sorry to butt in..but I want to understand differential equations better, if you use the integrating factor do you multiply by all the terms? how would you proceed from here?
Multiply both sides by $x^2$. That's the only way to make sure the equation still says the same thing.
$\frac{dy}{dx} + \frac{2}{x} \, y = \frac{5}{x^3}$

$x^2 \cdot \frac{dy}{dx} + x^2 \cdot \frac{2}{x} \, y = x^2 \cdot \frac{5}{x^3}$

$x^2 \cdot \frac{dy}{dx} + 2xy = \frac{5}{x}$

$\frac{d}{dx} \left ( x^2y \right ) = \frac{5}{x}$

Now integrate both sides with respect to x:
$x^2y = 5~ln(x) + C$

You take it from here.

-Dan