What are Degree and Order of a differential equation?
$begingroup$
What are Degree and Order of a differential equation?
I started reading ODE. I encountered this topic. But I saw there are many cases when Degree can not be determined.
So can anyone explain the following questions extensively? I want to understand ------
1) What are they?
2) Why they were introduced?
3) When either Degree or order or both can not be determined?
What I understood: $log (frac{dy}{dx})^2 + 7 (frac{dy}{dx})^2 cosx(frac{d^2y}{dx^2})^2 +xy cosxy $
I can say that the order of this differential equation is 2. But Degree can not be determined as $ cos(x(frac{d^2y}{dx^2})^2)$ is an infinite series of $x(frac{d^2y}{dx^2})^2$.
Have I gone wrong anywhere?
ordinary-differential-equations
asked Dec 21 '18 at 5:24
cmicmi
1,120312
$endgroup$
add a comment |
$begingroup$
What are Degree and Order of a differential equation?
I started reading ODE. I encountered this topic. But I saw there are many cases when Degree can not be determined.
So can anyone explain the following questions extensively? I want to understand ------
1) What are they?
2) Why they were introduced?
3) When either Degree or order or both can not be determined?
What I understood: $log (frac{dy}{dx})^2 + 7 (frac{dy}{dx})^2 cosx(frac{d^2y}{dx^2})^2 +xy cosxy $
I can say that the order of this differential equation is 2. But Degree can not be determined as $ cos(x(frac{d^2y}{dx^2})^2)$ is an infinite series of $x(frac{d^2y}{dx^2})^2$.
Have I gone wrong anywhere?
ordinary-differential-equations
asked Dec 21 '18 at 5:24
cmicmi
1,120312
$endgroup$
1
$begingroup$
Are you sure it is not $$ color{blue}{left[cos x right]} color{red}{left(frac{{rm d}^2y}{{rm d}x^2}right)^2} $$ ?
$endgroup$
– caverac
Dec 21 '18 at 7:54
2
$begingroup$
The order is useful as it equals the number of boundary conditions you will need. First degree leaves you hopeful that you can solve it. Higher degrees signals its time to move on to the next problem!!!
$endgroup$
– user121049
Dec 21 '18 at 8:32
$begingroup$
edited..Please have a look.@caverac
$endgroup$
– cmi
Dec 21 '18 at 9:52
add a comment |
$begingroup$
What are Degree and Order of a differential equation?
I started reading ODE. I encountered this topic. But I saw there are many cases when Degree can not be determined.
So can anyone explain the following questions extensively? I want to understand ------
1) What are they?
2) Why they were introduced?
3) When either Degree or order or both can not be determined?
What I understood: $log (frac{dy}{dx})^2 + 7 (frac{dy}{dx})^2 cosx(frac{d^2y}{dx^2})^2 +xy cosxy $
I can say that the order of this differential equation is 2. But Degree can not be determined as $ cos(x(frac{d^2y}{dx^2})^2)$ is an infinite series of $x(frac{d^2y}{dx^2})^2$.
Have I gone wrong anywhere?
ordinary-differential-equations
asked Dec 21 '18 at 5:24
cmicmi
1,120312
$endgroup$
What are Degree and Order of a differential equation?
I started reading ODE. I encountered this topic. But I saw there are many cases when Degree can not be determined.
So can anyone explain the following questions extensively? I want to understand ------
1) What are they?
2) Why they were introduced?
3) When either Degree or order or both can not be determined?
What I understood: $log (frac{dy}{dx})^2 + 7 (frac{dy}{dx})^2 cosx(frac{d^2y}{dx^2})^2 +xy cosxy $
I can say that the order of this differential equation is 2. But Degree can not be determined as $ cos(x(frac{d^2y}{dx^2})^2)$ is an infinite series of $x(frac{d^2y}{dx^2})^2$.
Have I gone wrong anywhere?
ordinary-differential-equations
ordinary-differential-equations
asked Dec 21 '18 at 5:24
cmicmi
1,120312
asked Dec 21 '18 at 5:24
cmicmi
1,120312
edited Dec 21 '18 at 9:51
cmi
asked Dec 21 '18 at 5:24
cmicmi
1,120312
asked Dec 21 '18 at 5:24
cmicmi
1,120312
asked Dec 21 '18 at 5:24
cmicmi
1,120312
1,120312
1
$begingroup$
Are you sure it is not $$ color{blue}{left[cos x right]} color{red}{left(frac{{rm d}^2y}{{rm d}x^2}right)^2} $$ ?
$endgroup$
– caverac
Dec 21 '18 at 7:54
2
$begingroup$
The order is useful as it equals the number of boundary conditions you will need. First degree leaves you hopeful that you can solve it. Higher degrees signals its time to move on to the next problem!!!
$endgroup$
– user121049
Dec 21 '18 at 8:32
$begingroup$
edited..Please have a look.@caverac
$endgroup$
– cmi
Dec 21 '18 at 9:52
add a comment |
1
$begingroup$
Are you sure it is not $$ color{blue}{left[cos x right]} color{red}{left(frac{{rm d}^2y}{{rm d}x^2}right)^2} $$ ?
$endgroup$
– caverac
Dec 21 '18 at 7:54
2
$begingroup$
The order is useful as it equals the number of boundary conditions you will need. First degree leaves you hopeful that you can solve it. Higher degrees signals its time to move on to the next problem!!!
$endgroup$
– user121049
Dec 21 '18 at 8:32
$begingroup$
edited..Please have a look.@caverac
$endgroup$
– cmi
Dec 21 '18 at 9:52
1
1
$begingroup$
Are you sure it is not $$ color{blue}{left[cos x right]} color{red}{left(frac{{rm d}^2y}{{rm d}x^2}right)^2} $$ ?
$endgroup$
– caverac
Dec 21 '18 at 7:54
$begingroup$
Are you sure it is not $$ color{blue}{left[cos x right]} color{red}{left(frac{{rm d}^2y}{{rm d}x^2}right)^2} $$ ?
$endgroup$
– caverac
Dec 21 '18 at 7:54
2
2
$begingroup$
The order is useful as it equals the number of boundary conditions you will need. First degree leaves you hopeful that you can solve it. Higher degrees signals its time to move on to the next problem!!!
$endgroup$
– user121049
Dec 21 '18 at 8:32
$begingroup$
The order is useful as it equals the number of boundary conditions you will need. First degree leaves you hopeful that you can solve it. Higher degrees signals its time to move on to the next problem!!!
$endgroup$
– user121049
Dec 21 '18 at 8:32
$begingroup$
edited..Please have a look.@caverac
$endgroup$
– cmi
Dec 21 '18 at 9:52
$begingroup$
edited..Please have a look.@caverac
$endgroup$
– cmi
Dec 21 '18 at 9:52
add a comment |
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1
$begingroup$
Are you sure it is not $$ color{blue}{left[cos x right]} color{red}{left(frac{{rm d}^2y}{{rm d}x^2}right)^2} $$ ?
$endgroup$
– caverac
Dec 21 '18 at 7:54
2
$begingroup$
The order is useful as it equals the number of boundary conditions you will need. First degree leaves you hopeful that you can solve it. Higher degrees signals its time to move on to the next problem!!!
$endgroup$
– user121049
Dec 21 '18 at 8:32
$begingroup$
edited..Please have a look.@caverac
$endgroup$
– cmi
Dec 21 '18 at 9:52