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 July 3rd, 2016, 07:54 AM #1 Newbie   Joined: Oct 2014 From: 192.168.0.1 Posts: 13 Thanks: 2 Why this diff. equation does not have a degree? In a book, it was stated that the following equation is of second order but no degree since the equation cannot be rationalized. $\displaystyle t\left ( \frac{\mathrm{d^2} y}{\mathrm{d} t^2} \right )+t^{2}\frac{\mathrm{d} y}{\mathrm{d} t}-\left ( cost \right )\sqrt{y}=2t^{2}-3t+4$ Why cannot we rearrange the equation as follows: $\displaystyle t\left ( \frac{\mathrm{d^2} y}{\mathrm{d} t^2} \right )+t^{2}\frac{\mathrm{d} y}{\mathrm{d} t}-2t^{2}+3t-4=\left ( cost \right )\sqrt{y}$ Then, square both the sides to get the following: $\displaystyle \left ( t\left ( \frac{\mathrm{d^2} y}{\mathrm{d} t^2} \right )+t^{2}\frac{\mathrm{d} y}{\mathrm{d} t}-2t^{2}+3t-4 \right )^{2}=\left ( cos^{2}t \right )y$ Can't we say that the above equation is of second order and second degree? July 4th, 2016, 09:07 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 The equation, as it stands, is not a polynomial in y or its derivatives because of the $\displaystyle \sqrt{y}$. Squaring the equation eliminates the square root but then it is not the same equation, just as x= 1 is not the same equation as $\displaystyle x^2= 1$! Tags degree, diff, differential, equation, no degree 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 AhmedHelal Calculus 1 November 16th, 2015 01:28 PM mona123 Differential Equations 3 April 20th, 2015 10:13 AM Hatmpatn Differential Equations 5 December 16th, 2014 08:12 AM Dacu Algebra 8 July 10th, 2013 12:52 PM zgonda Calculus 1 November 27th, 2010 04:23 PM

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