Solving Non-Linear First order ODEsFirst order non linear Ordinary differential equationsSolving first order non linear ODEA second order linear ordinary differential equationFirst order non-linear differential equationSolving first order non linear equationSolving non-linear second order ODEsNon linear first order ODE, not exact and not separableSolving non-linear ODEsSolving Higher Order Partial Differential EquationIs this an exact differential equation or a first order non-linear ordinary differential equation?
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Solving Non-Linear First order ODEs
First order non linear Ordinary differential equationsSolving first order non linear ODEA second order linear ordinary differential equationFirst order non-linear differential equationSolving first order non linear equationSolving non-linear second order ODEsNon linear first order ODE, not exact and not separableSolving non-linear ODEsSolving Higher Order Partial Differential EquationIs this an exact differential equation or a first order non-linear ordinary differential equation?
$begingroup$
The equation is:
$$fracdxdt = beta + alphax(1 - fracxkappa) - x(mu + nu + delta)$$
$beta, alpha, kappa, mu, nu, delta$ are all constants.
I am trying to solve this differential equation.
I understand that this is a non-linear, first order differential equation, however it is non-separable due to the logistic component.
I don't think it is exact either so I don't know what to do now.
Any help would be appreciated.
ordinary-differential-equations
asked Mar 13 at 10:44
EmmaEmma
274
New contributor
Emma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
The equation is:
$$fracdxdt = beta + alphax(1 - fracxkappa) - x(mu + nu + delta)$$
$beta, alpha, kappa, mu, nu, delta$ are all constants.
I am trying to solve this differential equation.
I understand that this is a non-linear, first order differential equation, however it is non-separable due to the logistic component.
I don't think it is exact either so I don't know what to do now.
Any help would be appreciated.
ordinary-differential-equations
asked Mar 13 at 10:44
EmmaEmma
274
New contributor
Emma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Am I right to say that it takes the form of a Riccati differential equation if the logistic component is expanded out? Is there a technique used to solve Riccati differential equations?
$endgroup$
– Emma
Mar 13 at 11:03
add a comment |
$begingroup$
The equation is:
$$fracdxdt = beta + alphax(1 - fracxkappa) - x(mu + nu + delta)$$
$beta, alpha, kappa, mu, nu, delta$ are all constants.
I am trying to solve this differential equation.
I understand that this is a non-linear, first order differential equation, however it is non-separable due to the logistic component.
I don't think it is exact either so I don't know what to do now.
Any help would be appreciated.
ordinary-differential-equations
asked Mar 13 at 10:44
EmmaEmma
274
New contributor
Emma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
The equation is:
$$fracdxdt = beta + alphax(1 - fracxkappa) - x(mu + nu + delta)$$
$beta, alpha, kappa, mu, nu, delta$ are all constants.
I am trying to solve this differential equation.
I understand that this is a non-linear, first order differential equation, however it is non-separable due to the logistic component.
I don't think it is exact either so I don't know what to do now.
Any help would be appreciated.
ordinary-differential-equations
ordinary-differential-equations
asked Mar 13 at 10:44
EmmaEmma
274
New contributor
Emma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 13 at 10:44
EmmaEmma
274
New contributor
Emma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 13 at 10:44
EmmaEmma
274
New contributor
Emma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 13 at 10:44
EmmaEmma
274
asked Mar 13 at 10:44
EmmaEmma
274
274
New contributor
Emma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Emma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Emma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
Am I right to say that it takes the form of a Riccati differential equation if the logistic component is expanded out? Is there a technique used to solve Riccati differential equations?
$endgroup$
– Emma
Mar 13 at 11:03
add a comment |
$begingroup$
Am I right to say that it takes the form of a Riccati differential equation if the logistic component is expanded out? Is there a technique used to solve Riccati differential equations?
$endgroup$
– Emma
Mar 13 at 11:03
$begingroup$
Am I right to say that it takes the form of a Riccati differential equation if the logistic component is expanded out? Is there a technique used to solve Riccati differential equations?
$endgroup$
– Emma
Mar 13 at 11:03
$begingroup$
Am I right to say that it takes the form of a Riccati differential equation if the logistic component is expanded out? Is there a technique used to solve Riccati differential equations?
$endgroup$
– Emma
Mar 13 at 11:03
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The equation is nonlinear, but it is separable, as it has the form
$$
fractextd xtextd t = f(x).
$$
Therefore, all you have to do is to solve the equation
$$
int^x frac1f(hatx)textdhatx = t + t_0
$$
for $x$. You will obtain something of the form
$$
x(t) = c_1 + c_2 ,texttanh left(c_3(t+t_0)right),
$$
where $c_1,c_2,c_3$ are constants depending on the model parameters $alpha,beta,delta,kappa,mu,nu$.
answered Mar 13 at 11:17
Frits VeermanFrits Veerman
7,0312921
$endgroup$
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The equation is nonlinear, but it is separable, as it has the form
$$
fractextd xtextd t = f(x).
$$
Therefore, all you have to do is to solve the equation
$$
int^x frac1f(hatx)textdhatx = t + t_0
$$
for $x$. You will obtain something of the form
$$
x(t) = c_1 + c_2 ,texttanh left(c_3(t+t_0)right),
$$
where $c_1,c_2,c_3$ are constants depending on the model parameters $alpha,beta,delta,kappa,mu,nu$.
answered Mar 13 at 11:17
Frits VeermanFrits Veerman
7,0312921
$endgroup$
add a comment |
$begingroup$
The equation is nonlinear, but it is separable, as it has the form
$$
fractextd xtextd t = f(x).
$$
Therefore, all you have to do is to solve the equation
$$
int^x frac1f(hatx)textdhatx = t + t_0
$$
for $x$. You will obtain something of the form
$$
x(t) = c_1 + c_2 ,texttanh left(c_3(t+t_0)right),
$$
where $c_1,c_2,c_3$ are constants depending on the model parameters $alpha,beta,delta,kappa,mu,nu$.
answered Mar 13 at 11:17
Frits VeermanFrits Veerman
7,0312921
$endgroup$
add a comment |
$begingroup$
The equation is nonlinear, but it is separable, as it has the form
$$
fractextd xtextd t = f(x).
$$
Therefore, all you have to do is to solve the equation
$$
int^x frac1f(hatx)textdhatx = t + t_0
$$
for $x$. You will obtain something of the form
$$
x(t) = c_1 + c_2 ,texttanh left(c_3(t+t_0)right),
$$
where $c_1,c_2,c_3$ are constants depending on the model parameters $alpha,beta,delta,kappa,mu,nu$.
answered Mar 13 at 11:17
Frits VeermanFrits Veerman
7,0312921
$endgroup$
The equation is nonlinear, but it is separable, as it has the form
$$
fractextd xtextd t = f(x).
$$
Therefore, all you have to do is to solve the equation
$$
int^x frac1f(hatx)textdhatx = t + t_0
$$
for $x$. You will obtain something of the form
$$
x(t) = c_1 + c_2 ,texttanh left(c_3(t+t_0)right),
$$
where $c_1,c_2,c_3$ are constants depending on the model parameters $alpha,beta,delta,kappa,mu,nu$.
answered Mar 13 at 11:17
Frits VeermanFrits Veerman
7,0312921
answered Mar 13 at 11:17
Frits VeermanFrits Veerman
7,0312921
answered Mar 13 at 11:17
Frits VeermanFrits Veerman
7,0312921
answered Mar 13 at 11:17
Frits VeermanFrits Veerman
7,0312921
7,0312921
add a comment |
add a comment |
Emma is a new contributor. Be nice, and check out our Code of Conduct.
Emma is a new contributor. Be nice, and check out our Code of Conduct.
Emma is a new contributor. Be nice, and check out our Code of Conduct.
Emma is a new contributor. Be nice, and check out our Code of Conduct.
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$begingroup$
Am I right to say that it takes the form of a Riccati differential equation if the logistic component is expanded out? Is there a technique used to solve Riccati differential equations?
$endgroup$
– Emma
Mar 13 at 11:03