Boundedness of the solutions of the equation $y'' + x y = 0 $ as $x rightarrow +infty$Behaviour of Solutions to $x^2y'' + alpha xy'+ beta y = 0$ as $x to 0$ and $x to infty$Modified Airy differential equationHow to show that all solutions of $ay''+by'+cy=0$ approach $0$ as $t rightarrow infty$Existence and Uniqueness of solutions to a differential equation.How do I solve for simple pendulum?Inhomogeneous Airy EquationUnderstanding solutions to the Mathieu Equation in the context of Classical MechanicsBehavior of the solution of the equation $f'' = -x f $ as $xrightarrow infty$Boundedness of Solutions of Differential EquationNonstandard independent solutions of the Airy equation
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Boundedness of the solutions of the equation $y'' + x y = 0 $ as $x rightarrow +infty$
Behaviour of Solutions to $x^2y'' + alpha xy'+ beta y = 0$ as $x to 0$ and $x to infty$Modified Airy differential equationHow to show that all solutions of $ay''+by'+cy=0$ approach $0$ as $t rightarrow infty$Existence and Uniqueness of solutions to a differential equation.How do I solve for simple pendulum?Inhomogeneous Airy EquationUnderstanding solutions to the Mathieu Equation in the context of Classical MechanicsBehavior of the solution of the equation $f'' = -x f $ as $xrightarrow infty$Boundedness of Solutions of Differential EquationNonstandard independent solutions of the Airy equation
$begingroup$
This is the Airy equation. We know that the two solutions are both bounded as $xrightarrow infty$.
The picture is that the solution just oscillates with higher and higher frequency ($propto sqrtx$) but its amplitude does not increase.
Can we develop this into a general theorem?
Are the solutions of the equation $y''+ x^2 y = 0 $ bounded in both directions?
ordinary-differential-equations
asked Mar 17 at 23:28
JohnJohn
1874
$endgroup$
add a comment |
$begingroup$
This is the Airy equation. We know that the two solutions are both bounded as $xrightarrow infty$.
The picture is that the solution just oscillates with higher and higher frequency ($propto sqrtx$) but its amplitude does not increase.
Can we develop this into a general theorem?
Are the solutions of the equation $y''+ x^2 y = 0 $ bounded in both directions?
ordinary-differential-equations
asked Mar 17 at 23:28
JohnJohn
1874
$endgroup$
$begingroup$
Look up perturbation theory.
$endgroup$
– MachineLearner
Mar 17 at 23:30
add a comment |
$begingroup$
This is the Airy equation. We know that the two solutions are both bounded as $xrightarrow infty$.
The picture is that the solution just oscillates with higher and higher frequency ($propto sqrtx$) but its amplitude does not increase.
Can we develop this into a general theorem?
Are the solutions of the equation $y''+ x^2 y = 0 $ bounded in both directions?
ordinary-differential-equations
asked Mar 17 at 23:28
JohnJohn
1874
$endgroup$
This is the Airy equation. We know that the two solutions are both bounded as $xrightarrow infty$.
The picture is that the solution just oscillates with higher and higher frequency ($propto sqrtx$) but its amplitude does not increase.
Can we develop this into a general theorem?
Are the solutions of the equation $y''+ x^2 y = 0 $ bounded in both directions?
ordinary-differential-equations
ordinary-differential-equations
asked Mar 17 at 23:28
JohnJohn
1874
asked Mar 17 at 23:28
JohnJohn
1874
asked Mar 17 at 23:28
JohnJohn
1874
asked Mar 17 at 23:28
JohnJohn
1874
asked Mar 17 at 23:28
JohnJohn
1874
1874
$begingroup$
Look up perturbation theory.
$endgroup$
– MachineLearner
Mar 17 at 23:30
add a comment |
$begingroup$
Look up perturbation theory.
$endgroup$
– MachineLearner
Mar 17 at 23:30
$begingroup$
Look up perturbation theory.
$endgroup$
– MachineLearner
Mar 17 at 23:30
$begingroup$
Look up perturbation theory.
$endgroup$
– MachineLearner
Mar 17 at 23:30
add a comment |
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$begingroup$
Look up perturbation theory.
$endgroup$
– MachineLearner
Mar 17 at 23:30