Learning DEs: Solving 2nd Order Differential Equations

In summary, the conversation discusses the process of solving a second-order differential equation to obtain the equation of motion. The question is asked about the procedure for obtaining the equation of motion from Newton's second law of motion, and the answer is given that it can be solved by integrating twice on both sides.
  • #1
greg_rack
Gold Member
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Hi guys,

I have just started studying DEs on my own, so pardonne moi in advance for the probably silly question :)

Via Newton's second law of motion:
$$x''=\frac{F}{m} \ [1]$$
Which is a second-order differential equation.
But, from here, how do I get the good old equation of motion:
$$x(t)=\frac{F}{2m}t^2+vt+x$$
by solving the DE? What is the procedure to apply? In my textbook, only second-order homogeneous DE are treated, but nothing with the form of ##[1]##... and online everything looks over-complicated.
 
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  • #2
Ok, I managed to get to the solution just by integrating twice both sides.
I was wrapping my head for nothing!
 
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FAQ: Learning DEs: Solving 2nd Order Differential Equations

What is a 2nd order differential equation?

A 2nd order differential equation is a mathematical equation that involves the second derivative of a function. It is used to describe the relationship between a function and its derivatives.

How do you solve a 2nd order differential equation?

To solve a 2nd order differential equation, you can use various methods such as separation of variables, substitution, or the method of undetermined coefficients. It is important to first identify the type of differential equation and then choose the appropriate method to solve it.

What are the applications of 2nd order differential equations?

2nd order differential equations have a wide range of applications in physics, engineering, and other fields. They are used to model systems that involve acceleration, such as motion of objects, electrical circuits, and chemical reactions.

Can 2nd order differential equations have multiple solutions?

Yes, 2nd order differential equations can have multiple solutions. This is because the general solution of a 2nd order differential equation contains two arbitrary constants, which can result in different solutions depending on the initial conditions given.

What are some common mistakes when solving 2nd order differential equations?

Some common mistakes when solving 2nd order differential equations include forgetting to include the constant of integration, making errors in algebraic manipulations, and using the wrong method to solve the equation. It is important to double-check your work and be familiar with the different methods of solving these equations.

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