Help in solving a Differential Equation

**sashikanth** · December 14th 2010, 06:10 AM

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

**Danny** · December 14th 2010, 07:16 AM

First write your ODE as

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

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

which is of the form

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

If $\dfrac{M_y-N_x}{N} = Q(x)$ then $\mu = e^{\int Q(x)dx}$ is an integrating factor.

**sashikanth** · December 14th 2010, 07:38 AM

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 $\frac{x}{y} = \tan{\theta}$ , I tried doing that to no avail.

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