# Y''(x) + A sin(y(x)) - B = 0; A,B : positive, real

• tarquinius
In summary, the conversation is about a differential equation that the speaker is struggling to solve. They provide the equation, initial conditions, and express their gratitude for any help. The equation cannot be solved using traditional methods due to the presence of non-standard functions.
tarquinius
Hello there,

I have no idea how to solve the differential equation

y''(x) + A sin(y(x)) - B = 0 ,

where A and B are positive real numbers. I do also have initial conditions: y(0) = 0 and y'(0) = 0.

I would be grateful for any help.

y''+A sin(y)-B=0
y''y'+A sin(y)y'-B y'=0
y'²/2-A cos(y)-B y =C
y'²=2A cos(y)+2B y +2C
dy/dx =y' = (+or-)sqrt(2A cos(y)+2B y+2C)
dx=(+or-) dy/sqrt(2A cos(y)+2B y+2C)
x =(+or-) integal (dy/sqrt(2A cos(y)+2B y+2C)) +c
cannot be expressed with a finit number of usual functions;

Thank you very much.

## 1. What is the purpose of the equation "Y''(x) + A sin(y(x)) - B = 0"?

The equation represents a mathematical model used to describe the behavior of a system with two variables, y and x. It is commonly used in physics and engineering to study oscillatory systems.

## 2. What do the variables A, B, and x represent in the equation?

A and B are positive, real constants that affect the amplitude and phase shift of the oscillations described by the equation. X represents the independent variable, typically time, and y(x) is the dependent variable.

## 3. How is the equation solved?

The equation can be solved analytically using mathematical techniques such as separation of variables or by using numerical methods such as Euler's method or Runge-Kutta methods. The specific method used depends on the initial conditions and the desired level of accuracy.

## 4. What are the physical applications of this equation?

This equation has many real-world applications, including modeling the motion of a pendulum, describing the oscillations of a spring, analyzing electrical circuits, and understanding the behavior of waves in various systems.

## 5. Can this equation be generalized to include more variables?

Yes, this equation can be extended to include more variables, such as higher-order derivatives or additional trigonometric terms. This allows for a more complex and accurate description of the behavior of various systems.

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