3
$\begingroup$

I'm trying to solve $$\sin(x)\frac{d}{dx}\beta \left ( x \right )+\cos(x)\beta (x)=1$$ What I get is : $$\beta (x)=\beta \left ( \alpha \right )e^{\sin(\alpha )-\sin(x)}+e^{-\sin(x)}\int_{\alpha }^{x}e^{\sin(t)}dt$$ But I think that this solution is incorrect .The textbook says that there's exactly one solution that has a finite limit as $x$ tends to $0$ . But all the solutions I get have a finite limit . So what's the correct solution?

  • 0
    Note that you can use \sin, \cos for the $\sin,\cos$ functions. see the difference between $sin(x)$ and $\sin(x)$2012-11-03
  • 0
    Unless $\beta(x)$ is a special function, I see that since $sin^2(x)+cos^2(x)=1$ which makes $\beta(x)=cos(x)$ is a solution.2012-11-03
  • 1
    @EmmadKareem That was my first thought, but it gives $-\sin^2(x)+\cos^2(x)$, notice the "negative sign" (pun!)2012-11-03
  • 0
    @Logan, thanks, I need thicker glasses and a new brain :)2012-11-03

1 Answers 1