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Help implementing DSolve on differential equations

Hengameh Bagherianlemraski
Posted 10 years ago

hello guys, I'm pretty new to mathematica! I'm trying to plot the system of differential equations below:

system = {x' == 1-y , y' == x^2 - y^2, {x,y} , t}

can u please help me with the code? I've tried to solve it numerically with Dsolve like below:

sol = DSolve { y' =(x^2-y^2)/(1-y) , y[0] ==1 , y'[0]==2}

but my mathematica doesn't catch the first part for some reason it just keeps evaluating it to true :\ i would be grateful if u guys could help me with this :)
POSTED BY: Hengameh Bagherianlemraski
4 Replies
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POSTED BY: Mariusz Iwaniuk

Thank you so much it helped! but why does it tell me: NDSolve::icordinit: The initial values for all the dependent variables are not explicitly specified. NDSolve will attempt to find consistent initial conditions for all the variables. >>!and also is there anyway to plot some other curves with random initial value conditions?enter image description here
POSTED BY: Hengameh Bagherianlemraski

Maybe this helps:

system = {x'[t] == 1 - y[t], y'[t] == x[t]^2 - y[t]^2};
ibc = {y[0] == 1, y'[0] == 2};
sol = NDSolve[{system, ibc}, {x[t], y[t]}, {t, 0, 5}];
Plot[Evaluate[{x[t], y[t]} /. sol], {t, 0, 5},PlotLegends -> {"x[t]", "y[t]"}, PlotRange -> All]

enter image description here
POSTED BY: Mariusz Iwaniuk

The independent variable t must be explicit: x[t], y[t], x'[t]. y'[t], and not just x,y,x',y'.
POSTED BY: Gianluca Gorni
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