sec(x) dy/dx = e^(y + sin(x))

So far I have :

ln (secx) dy/dx = y + sin x

ln (secx) dy = y + sinx dx

Not sure what to do now... I don't think I can just subtract the y?

Printable View

- Oct 20th 2008, 08:23 PMveronicak5678Solve the Differential Equation
sec(x) dy/dx = e^(y + sin(x))

So far I have :

ln (secx) dy/dx = y + sin x

ln (secx) dy = y + sinx dx

Not sure what to do now... I don't think I can just subtract the y? - Oct 20th 2008, 08:44 PMlllll
you should be able to solve this using implicit differentiation.

so you have $\displaystyle \frac{dy}{dx} = -\frac{\frac{\partial F}{\partial x}}{\frac{\partial F}{\partial y}} = -\frac{F_x}{F_y} $

so then

$\displaystyle \sec(x) dy/dx = e^{y + \sin(x)}$

$\displaystyle = \frac{1}{\cos(x)} \frac{dy}{dx} = e^{y + \sin(x)} $

$\displaystyle \frac{dy}{dx}= e^{y + \sin(x)} \times \cos(x)$

$\displaystyle \frac{\partial F}{\partial y} = e^{y + \sin(x)} \times \cos(x)$

$\displaystyle \frac{\partial F}{\partial x} = \cos(x) \times e^{y + \sin(x)} \times \cos(x) -sin(x) \times e^{y + \sin(x)} = e^{y + \sin(x)}(\cos^2(x) -\sin(x))$

now just combine both function... - Oct 20th 2008, 08:45 PMChris L T521
- Oct 20th 2008, 08:58 PMveronicak5678
I see. Thanks!

- Oct 20th 2008, 09:01 PMChris L T521