# Second-Order separable Differential equations

• Woolyabyss
In summary, the conversation is about a problem with a typo in the equation and the difficulty is that there is only one equation for two unknown functions. It is suggested to clarify the problem before proceeding.

## Homework Statement

Solve d2y/dt2 = dx/dt2, if x = 0 and dx/dt = 1 when t = 0

## The Attempt at a Solution

d2y = dx

I'm not exactly sure what to do here the fact that dt2 is under the denominator for both fractions is confusing memaybe its a typo? should it be d2y/dx2 = dx/dt?

Woolyabyss said:

## Homework Statement

Solve d2y/dt2 = dx/dt2, if x = 0 and dx/dt = 1 when t = 0

## The Attempt at a Solution

d2y = dx

I'm not exactly sure what to do here the fact that dt2 is under the denominator for both fractions is confusing memaybe its a typo? should it be d2y/dx2 = dx/dt?
That has to be a typo. dx/dt2 makes zero sense.

On a side note, try to make you posts clearer by at least indicating that some things are exponents. The simplest way is to use the caret or circumflex character (^), which is pretty much universally used for this purpose. For example, 3x2 and e^(rt).

A little nicer is to use the advanced menu (click Go Advanced below the input area. For exponents, click the X2 button. You can do subscripts with the X2 button.

For fancier stuff, you can use LaTeX to write things like ##10x^2## and even fancier stuff. Here's a link to a summary of how to do that: https://www.physicsforums.com/showthread.php?t=617567 - item 2 on the list.

Mark44 said:
That has to be a typo. dx/dt2 makes zero sense.

On a side note, try to make you posts clearer by at least indicating that some things are exponents. The simplest way is to use the caret or circumflex character (^), which is pretty much universally used for this purpose. For example, 3x2 and e^(rt).

A little nicer is to use the advanced menu (click Go Advanced below the input area. For exponents, click the X2 button. You can do subscripts with the X2 button.

For fancier stuff, you can use LaTeX to write things like ##10x^2## and even fancier stuff. Here's a link to a summary of how to do that: https://www.physicsforums.com/showthread.php?t=617567 - item 2 on the list.

Alright thanks, If i were to assume they meant d^2y/dt^2 = dx/dt

would I be correct in saying I could integrate both sides and it would be dy/dt = x + c?

It might be better to figure out what the exact problem should be. Can you contact your instructor to get this clarified?

Mark44 said:
It might be better to figure out what the exact problem should be. Can you contact your instructor to get this clarified?

No I am afraid not I'll just leave ut for now. Thans anyway

The difficulty is that you have a single equation for two unknown functions, x and y. That is not sufficient. You need another equation.

## 1. What is a second-order separable differential equation?

A second-order separable differential equation is a type of differential equation in which the second derivative of the dependent variable can be expressed as a product of two functions, each of which depends on only one of the independent variables.

## 2. What is the general form of a second-order separable differential equation?

The general form of a second-order separable differential equation is y'' = f(x)g(y), where f(x) and g(y) are functions of x and y, respectively.

## 3. How do you solve a second-order separable differential equation?

To solve a second-order separable differential equation, first separate the variables by moving all terms involving y'' to one side and all terms involving x to the other side. Then, integrate both sides with respect to their respective variables. Finally, solve for y using algebraic manipulation.

## 4. What are some applications of second-order separable differential equations?

Second-order separable differential equations are commonly used in physics and engineering to model physical systems such as oscillating springs, pendulums, and electrical circuits. They are also used in economics to model population growth and in genetics to model population dynamics.

## 5. Are there any limitations to using second-order separable differential equations?

One limitation of using second-order separable differential equations is that not all physical systems can be accurately modeled using this technique. Additionally, some second-order separable differential equations may not have closed-form solutions and require numerical methods for approximation.