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 December 1st, 2011, 04:09 AM #1 Newbie   Joined: Dec 2011 Posts: 3 Thanks: 0 ordinary differential equation i want to solve the ODE y''=e^(-ay)
 December 1st, 2011, 08:19 AM #2 Senior Member   Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0 Re: ordinary differential equation $\frac{d^2y }{d x^2}\frac{dy }{d x}=e^{-ay}\frac{dy }{d x}$ $\frac{\mathrm{d} }{\mathrm{d} x}(\frac{1}{2} (\frac{dy }{d x})^{2})=\frac{-1}{a}\frac{de^{-ay} }{d x}$ $\frac{1}{2} (\frac{dy }{d x})^{2}=\frac{-1}{a}e^{-ay}+C_{0}$ $(\frac{dy }{d x})^{2}=\frac{-2}{a}e^{-ay}+2C_{0}$ $\frac{dy }{\sqrt{\frac{-2}{a}e^{-ay}+2C_{0}}}=dx$ $\int {\frac{dy }{\sqrt{\frac{-2}{a}e^{-ay}+2C_{0}}}}=x+C_{1}$ ...
 December 4th, 2011, 01:40 AM #3 Newbie   Joined: Dec 2011 Posts: 3 Thanks: 0 Re: ordinary differential equation thank you very much Mr. wnvl
 February 22nd, 2014, 07:03 AM #4 Newbie   Joined: Dec 2011 Posts: 3 Thanks: 0 Re: ordinary differential equation what is the analytical solution of this ODE: f'''+ 0.5 f f''=0, under : f'(0)=0,f(0)=0, Lim f(x) as x goes to infinity =1

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