TianyuCheng

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0 years, 132 days

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These are questions asked by TianyuCheng

I try to give the plot, but it shows nothing. why? How can l find the range where 2+r*(b-2)*sqrt(b-1) can be positive, and the range where 2+r*(b-2)*sqrt(b-1) can be negative?


 

restart; with(plots, implicitplot); implicitplot(2+r*(b-2)*sqrt(b-1), b = 1 .. 100, r = 1 .. 100, scaling = constrained)

 

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Why is my figure not smooth? How can I make it smooth?
 

with(plots, implicitplot); with(plots)

pp1 := implicitplot(mu*x-ln(1+x) = 0, mu = -10 .. 5, x = -5 .. 5, color = black)

 

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s1 := RootOf(D1*D2*D6*_Z^2+(-D1*D4*D6-D2*D6*S-D4)*_Z+D4*D6*S)

s2 := -(D1*RootOf(D1*D2*D6*_Z^2+(-D1*D4*D6-D2*D6*S-D4)*_Z+D4*D6*S)*D6-S*D6+RootOf(D1*D2*D6*_Z^2+(-D1*D4*D6-D2*D6*S-D4)*_Z+D4*D6*S))/(D2*D6*RootOf(D1*D2*D6*_Z^2+(-D1*D4*D6-D2*D6*S-D4)*_Z+D4*D6*S))
algsubs(s = RootOf(D1*D2*D6*_Z^2+(-D1*D4*D6-D2*D6*S-D4)*_Z+D4*D6*S), s2)

I try to use s1 to represent s2, and I get the following result:

-(D1*__SELECTION(RootOf(D1*D2*D6*_Z^2+(-D1*D4*D6-D2*D6*S-D4)*_Z+D4*D6*S))*D6-S*D6+RootOf(D1*D2*D6*_Z^2+(-D1*D4*D6-D2*D6*S-D4)*_Z+D4*D6*S))/(D2*D6*RootOf(D1*D2*D6*_Z^2+(-D1*D4*D6-D2*D6*S-D4)*_Z+D4*D6*S))
what is mean of __SELECTION, If algsubs cannot work well, what should I do?

I try to use phaseportrait to get the phase portrait of the following ode system, why it does not give the plot or the error reminding?


 

with(LinearAlgebra)

phaseportrait([diff(x(t), t) = -((y(t)^2*x(t)+x(t)^3+y(t)-x(t))*sqrt((y(t)^2+x(t)^2)/x(t)^2)-2*x(t))*x(t)/sqrt(y(t)^2+x(t)^2), diff(y(t), t) = -x(t)*((y(t)^3+y(t)*x(t)^2-y(t)-x(t))*sqrt((y(t)^2+x(t)^2)/x(t)^2)-2*y(t))/sqrt(y(t)^2+x(t)^2)], [x(t), y(t)], t = 0 .. 50, [[x(0) = -1, y(0) = -1], [x(0) = -5, y(0) = -5]], x = -10 .. 20, y = -10 .. 30, dirgrid = [40, 40], stepsize = 0.1e-2, numframes = 90, axes = BOXED, linecolor = black)

phaseportrait([diff(x(t), t) = -((y(t)^2*x(t)+x(t)^3+y(t)-x(t))*((y(t)^2+x(t)^2)/x(t)^2)^(1/2)-2*x(t))*x(t)/(y(t)^2+x(t)^2)^(1/2), diff(y(t), t) = -x(t)*((y(t)^3+y(t)*x(t)^2-y(t)-x(t))*((y(t)^2+x(t)^2)/x(t)^2)^(1/2)-2*y(t))/(y(t)^2+x(t)^2)^(1/2)], [x(t), y(t)], t = 0 .. 50, [[x(0) = -1, y(0) = -1], [x(0) = -5, y(0) = -5]], x = -10 .. 20, y = -10 .. 30, dirgrid = [40, 40], stepsize = 0.1e-2, numframes = 90, axes = BOXED, linecolor = black)

(1)

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Download m40.mw

 

solve it by Maple , get the following form solution, what's the Int(1,0)

 


 

restart;

 

ODE :=diff(r(t),t)=r(t)*(1-r(t)^2)+mu*r(t)*cos(t)

diff(r(t), t) = r(t)*(1-r(t)^2)+mu*r(t)*cos(t)

(1)

dsolve(ODE)

r(t) = ((_C1+2*(Int((exp(t))^2*(exp(mu*sin(t)))^2, t)))*exp(2*t+2*mu*sin(t)))^(1/2)/(_C1+2*(Int((exp(t))^2*(exp(mu*sin(t)))^2, t))), r(t) = -((_C1+2*(Int((exp(t))^2*(exp(mu*sin(t)))^2, t)))*exp(2*t+2*mu*sin(t)))^(1/2)/(_C1+2*(Int((exp(t))^2*(exp(mu*sin(t)))^2, t)))

(2)

g := unapply(sqrt((C1+2*(Int((exp(t))^2*(exp(mu*sin(t)))^2, t)))*exp(2*t+2*mu*sin(t)))/(C1+2*(Int((exp(t))^2*(exp(mu*sin(t)))^2, t))), t)

proc (t) options operator, arrow; ((C1+2*(Int((exp(t))^2*(exp(mu*sin(t)))^2, t)))*exp(2*t+2*mu*sin(t)))^(1/2)/(C1+2*(Int((exp(t))^2*(exp(mu*sin(t)))^2, t))) end proc

(3)

g(0)

1/(C1+2*(Int(1, 0)))^(1/2)

(4)

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