Help 2nd order ODE totally clueless

In summary, a 2nd order ODE is a mathematical equation that involves a function and its first and second derivatives. It can be solved analytically or numerically and is commonly used in physics, engineering, and other scientific fields. An example is the harmonic oscillator equation, and applications include mechanical systems, population growth, and chemical reactions. Resources for learning more about solving 2nd order ODEs include textbooks, online tutorials, and interactive software, as well as practice and guidance from a mentor or tutor.
  • #1
owlman76
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Find the general solution of

x2y'' + xy' + (x2 - 1/4)y = 0

and express it in terms of trigonometric functions. (You don't actually have to solve the equation from a trial function in this problem, but you must identify the differential equation. Then, you may write the solution and prove that it can be written as trigonometric functions.)
 
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1. What is a 2nd order ODE (ordinary differential equation)?

A 2nd order ODE is a mathematical equation that involves a function and its first and second derivatives. It is commonly used in physics, engineering, and other scientific fields to model systems that involve change over time.

2. How do I solve a 2nd order ODE?

Solving a 2nd order ODE involves finding a function that satisfies the equation. This can be done analytically using techniques such as separation of variables, or numerically using computational methods such as Euler's method or Runge-Kutta methods.

3. Can you provide an example of a 2nd order ODE?

One example of a 2nd order ODE is the harmonic oscillator equation, which describes the motion of a mass attached to a spring. It is given by the equation m(d^2x/dt^2) + kx = 0, where m is the mass, k is the spring constant, x is the displacement, and t is time.

4. What applications use 2nd order ODEs?

2nd order ODEs are used in a wide range of applications, including physics, engineering, economics, and biology. They can be used to model systems such as mechanical vibrations, electrical circuits, population growth, and chemical reactions.

5. What resources can I use to learn more about solving 2nd order ODEs?

There are many resources available for learning about 2nd order ODEs, including textbooks, online tutorials, and interactive software. Some recommended resources include "Ordinary Differential Equations" by Morris Tenenbaum and Harry Pollard, the Khan Academy Differential Equations course, and the ODE Toolkit software. It is also helpful to practice solving problems and seek guidance from a mentor or tutor.

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