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macik1423
 Post subject: Solve y'=e^x-y^2
PostPosted: Thu, 3 Nov 2011 20:37:44 UTC 
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Hi, i'm new in this forum. I need help with this equation:
y'=e^{x}-y^{2}, i have no idea how to do it.
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pickslides
 Post subject: Re: Solve y'=e^x-y^2
PostPosted: Thu, 3 Nov 2011 23:31:03 UTC 
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Have a read of this

http://www.sosmath.com/diffeq/first/ric ... ccati.html
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outermeasure
 Post subject: Re: Solve y'=e^x-y^2
PostPosted: Fri, 4 Nov 2011 07:03:03 UTC 
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macik1423 wrote:
Hi, i'm new in this forum. I need help with this equation:
y'=e^{x}-y^{2}, i have no idea how to do it.


According to Wolfram Alpha, you probably need the modified Bessel functions to solve this analytically.

_________________
\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
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