differential equations

**taurus** · June 5th 2008, 12:18 PM

Solve the following differential equations.

y' = ((y^2)+xy)/(x^2)

Whats the method of solving this? What theorem am i using?

**PaulRS** · June 5th 2008, 12:40 PM

First divide by $y^2$ both sides : $ \tfrac{{y'}} {{y^2 }} = \tfrac{1} {{x^2 }} + \tfrac{1} {x} \cdot \tfrac{1} {y} $

But note that: $ \tfrac{{y'}} {{y^2 }} = - \left( {\tfrac{1} {y}} \right)^\prime $

Let: $ \tfrac{1} {y} = z $ we have: $ - z' = \tfrac{1} {{x^2 }} + \tfrac{1} {x} \cdot z $

You can solve this last one by the integrating factor method

**taurus** · June 5th 2008, 12:49 PM

Why do you divide by Y^2?

**Krizalid** · June 5th 2008, 01:18 PM

$\frac{y^{2}+xy}{x^{2}}=\bigg( \frac{y}{x} \bigg)^{2}+\frac{y}{x}.$

Then let $y=xz.$

Thread: differential equations

LinkBack

Thread Tools

Display

differential equations

Similar Math Help Forum Discussions

'Differential' in differential equations

Differential Equations-Application of 1st order differential equations 1

Differential Equations

Differential Equations:Linear first Order Equations

First Order Differential Equations: Separable Equations and Applications

Search Tags