differential equation

**crafty** · February 5th 2009, 07:04 PM

(dy/dx) + x/y^3 = -3y/x how do i solve this?

**Danny** · February 6th 2009, 06:40 AM

Originally Posted by crafty

(dy/dx) + x/y^3 = -3y/x how do i solve this?

Standard form

$\frac{dy}{dx} + \frac{3y}{x} = - \frac{x}{y^3}$

Multiply by $y^3$

$y^3 \frac{dy}{dx} + \frac{3y^4}{x} = - x$

and make the substitution $u = y^4$ . The equation will become linear!

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