Theory of Differential Equations

Cover Theory of Differential Equations
Theory of Differential Equations
Forsyth, Andrew Russell, 1858-1942
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This subsidiary system contains 2ii differential equations: its integral equivalent must therefore contain 2ii integral equations, that is, it possesties 2a integrals. Hence there are sufficient integrals for the achievement of n stages ; at the end of the last, we shall have jafiinction of 0*1, ..., x^, Oi, ..., On,.
(where Oi, ..., On are arbitrary constants) as the integral of the original equation. Or at the completion of the (n — l)th stage, we can resolve the n equations then coexis
...ting, and express ji|, ...» jn^ in tonus of s, x^, ..., x^, (i„ ... , 0^.1 ; substitution in the relation and quadrature, lead t4) the integAl required.
Ex. Let JET denol« i-ih^i - ... -p»j*»; and supposs that a set of squatiuoii /;-/;(/>„ .... />„ Z)-0, 0»-l, .... m\ where m

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