Solve $\displaystyle \frac{dy}{dx} = \frac{x+ytany}{y-xtany} $

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- Dec 14th 2010, 06:10 AMsashikanthHelp in solving a Differential Equation
Solve $\displaystyle \frac{dy}{dx} = \frac{x+ytany}{y-xtany} $

- Dec 14th 2010, 07:16 AMJester
First write your ODE as

$\displaystyle (x + y \tan y)dx +(x \tan y - y)dy = 0$ then as

$\displaystyle (x \cos y + y \sin y)dx +(x \sin y - y \cos y)dy = 0$

which is of the form

$\displaystyle M(x,y)dx + N(x,y)dy = 0$. Then check $\displaystyle \dfrac{M_y-N_x}{N}$

If $\displaystyle \dfrac{M_y-N_x}{N} = Q(x)$ then $\displaystyle \mu = e^{\int Q(x)dx}$ is an integrating factor. - Dec 14th 2010, 07:38 AMsashikanth
Hi,

Thank you for your post! Is there any way I can do this problem without resorting to Integrating Factors? I'm just curious, the problem suggests you take $\displaystyle \frac{x}{y} = \tan{\theta} $ , I tried doing that to no avail.