# Differential Equations: $[x \csc (y/x) - y] dx + x \, dy = 0$

3 posts / 0 new
Sydney Sales
Differential Equations: $[x \csc (y/x) - y] dx + x \, dy = 0$

2. (x csc y/x - y) dx + xdy=0
3. (x^2 + 2xy - 4y^2) dx - ( x^2 - 8xy - 4 y^2)=0
4. x^y ' = 4x^2 + 7xy + 2 y^2

Jhun Vert

Solution (2)
$\left[ x \csc \left( \dfrac{y}{x} \right) - y \right] \, dx + x \, dy = 0$

Let y = vx
dy = v dx + x dv

$\left[ x \csc \left( \dfrac{vx}{x} \right) - vx \right] \, dx + x(v \, dx + x \, dv) = 0$

$(x \csc v - vx) \, dx + vx \, dx + x^2 \, dv = 0$

$x \csc v \, dx + x^2 \, dv = 0$

$\dfrac{dx}{x} + \dfrac{dv}{\csc v} = 0$

$\dfrac{dx}{x} + \sin v \, dv = 0$

$\ln x - \cos v = c$

$\ln x - \cos \left(\dfrac{y}{x} \right) = c$

Sydney Sales

thanks po sa solution.. yung prob. 3 and4. po...solution.

## Add new comment

### Deafult Input

• Allowed HTML tags: <img> <em> <strong> <cite> <code> <ul> <ol> <li> <dl> <dt> <dd> <sub> <sup> <blockquote> <ins> <del> <div>
• Web page addresses and e-mail addresses turn into links automatically.
• Lines and paragraphs break automatically.
• Mathematics inside the configured delimiters is rendered by MathJax. The default math delimiters are $$...$$ and $...$ for displayed mathematics, and $...$ and $...$ for in-line mathematics.

### Plain text

• No HTML tags allowed.
• Lines and paragraphs break automatically.