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 Differential Equations Ordinary and Partial Differential Equations Math Forum

 February 25th, 2019, 09:38 AM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 591 Thanks: 86 Non-order equation $\displaystyle y^{(1)} y^{(2)}\cdot .... \cdot y^{(n)} =e^{nx} \; \;$ , $\displaystyle n\in \mathbb{N}$ . Another way to write it better : $\displaystyle \prod_{i=1}^{n} \frac{d^i y}{dx^i } =e^{nx}$ . February 26th, 2019, 05:25 AM #2 Senior Member   Joined: Dec 2015 From: somewhere Posts: 591 Thanks: 86 Let $\displaystyle b_{n} =e^{nx}\; \;$ then $\displaystyle y^{(n+1)} =\frac{b_{n+1} }{b_n }=e^x$ . The equation $\displaystyle y^{(n+1)} =e^x \;$ has solution $\displaystyle y=c+e^x$. Tags equation, nonorder 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 Mrkukas Differential Equations 10 November 9th, 2016 03:12 AM idontknow Differential Equations 9 December 28th, 2015 02:50 PM eigenvexed Calculus 12 July 3rd, 2014 02:06 AM nehal Calculus 5 December 6th, 2013 04:20 PM shyjuu Calculus 3 June 27th, 2013 10:16 AM

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