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Question: find an explicit function of two functions of time.

Question:find an explicit function of two functions of time.

mehdi jafari 754 Maple
ode dsolve explicit differential-equations
November 12 2020
3

i have ode system of two dependent variables y and x  and one independent varibale time. how can i find explicit expression between y and x? 

 

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restart
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sys:=diff(x(t),t)=x(t)*y(t)+t,diff(y(t),t)=x(t)-t;

diff(x(t), t) = x(t)*y(t)+t, diff(y(t), t) = x(t)-t

 (1)
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dsolve([sys,x(0)=0,y(0)=1],[x(t),y(t)],series)

{x(t) = series((1/2)*t^2+(1/6)*t^3+(1/24)*t^4-(1/24)*t^5+O(t^6),t,6), y(t) = series(1-(1/2)*t^2+(1/6)*t^3+(1/24)*t^4+(1/120)*t^5+O(t^6),t,6)}

 (2)
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