Solving ODE with Constant Coefficients: A Scientific Approach

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In summary, the order of an ODE is determined by the highest derivative present in the equation, initial conditions are used to uniquely determine a solution to the ODE, not all ODEs have analytical solutions and may require numerical methods, a separable ODE can be solved by integrating and solving for the dependent variable, and an explicit solution is one where the dependent variable is explicitly written while an implicit solution requires solving the equation for the dependent variable.
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Mugged
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How do i solve this ODE, anyone have any ideas?

[tex] \frac{dv}{dt} = g - \frac{b}{m}*v^2 [/tex]
 
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  • #2


If g,b and m are constants, then a separation of variables method will work.
 
  • #3


yep they are constants. I made an attempt on this problem and got a function that includes the tan function. so i think I am ok
 
  • #4


Mugged said:
yep they are constants. I made an attempt on this problem and got a function that includes the tan function. so i think I am ok

You could have split the function into partial fractions if you wanted to.
 

1. How do I determine the order of an ODE?

The order of an ODE is determined by the highest derivative present in the equation. For example, if the equation contains a first derivative, it is a first-order ODE. If it contains a second derivative, it is a second-order ODE.

2. What are initial conditions in ODEs?

Initial conditions are the values of the dependent variable and its derivatives at a specified point in the independent variable. They are used to uniquely determine a solution to the ODE.

3. Can all ODEs be solved analytically?

No, not all ODEs have analytical solutions. Some ODEs may require numerical methods to find a solution.

4. How do I solve a separable ODE?

A separable ODE is one where the dependent variable and independent variable can be separated on opposite sides of the equation. To solve, you would integrate both sides and then solve for the dependent variable.

5. What is the difference between an explicit and implicit solution to an ODE?

An explicit solution is one where the dependent variable is explicitly written in terms of the independent variable. An implicit solution is one where the dependent variable is not explicitly written, but can be found by solving the equation for the dependent variable.

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