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Definition of equation of the first order, (second order, etc.) in US English:
equation of the first order, (second order, etc.)
phrase
Mathematics
An equation involving only the first derivative, second derivative, etc.
‘His doctoral dissertation was on the theory of the propeller which led to his developing a theory of partial differential equations of the second order.’
‘He began mathematical research while still an undergraduate and his first paper, On the isoclinal lines of a differential equation of the first order was published in the Proceedings of The Royal Society of Edinburgh in 1903.’
‘He did this by using an indeterminate equation of the second order, Nx 2 + 1 = y 2, where N is the number whose square root is to be calculated.’
‘Special attention should be drawn also to his little known pamphlet on regular point of linear differential equations of the second order used for a number of years in connection with one of his courses of lectures.’
‘This integral was introduced in a paper on differential equations of the second order which he wrote in 1870.’