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 Differential Equations Ordinary and Partial Differential Equations Math Forum

 October 7th, 2019, 08:53 AM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 734 Thanks: 98 Hard PDE Solve $\displaystyle \frac{\partial Z }{\partial x} =2x\cdot (1-\frac{\partial Z}{\partial y})\;$ , for $\displaystyle Z(x,0)=Z(0,y)=1$ . October 7th, 2019, 09:58 AM #2 Senior Member   Joined: Dec 2015 From: somewhere Posts: 734 Thanks: 98 $\displaystyle \mathscr{L} (z_x) +2x \mathscr{L} (z_y )=2x \mathscr{L}(1)$. $\displaystyle Z(x,y)=Ce^{-px^2 }+p^{-2}(1+p)=-e^{-px^2 }/p^{2}+p^{-2}(1+p)$. $\displaystyle \mathscr{L}^{-1} (Z)=-\mathscr{L}^{-1}(p^{-2} e^{-px^2 })+\mathscr{L}^{-1} (p^{-2})+\mathscr{L}^{-1}(1/p)$. $\displaystyle Z=-(y-x^2 )^{2} \int_{-\infty}^{x} \delta(s)ds+1+y$. Tags hard, pde Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Einsteinhelper Algebra 1 November 19th, 2015 01:09 PM roberthun Algebra 8 February 1st, 2013 08:31 AM ZardoZ Real Analysis 3 April 28th, 2011 04:43 PM themanandthe Algebra 9 April 26th, 2010 01:18 PM danyilmaz Applied Math 15 September 30th, 2009 08:20 AM

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