Differential equations - interval of existence

In summary, a differential equation is a mathematical equation that relates an unknown function to its derivatives. An interval of existence in a differential equation is the range of values for which a solution to the equation exists, typically expressed as a range of values for the independent variable. The interval of existence can be determined by analyzing the coefficients and initial conditions of the equation, as well as any restrictions on the independent variable. It is important because it provides information about the feasibility of the solution and can help make predictions about the behavior of the system. If the interval of existence is infinite, it means that the solution exists for all values of the independent variable, which is often the case for simple differential equations with no restrictions.
  • #1
pyroknife
613
3
dy/dx=(sinx)/y Initial condition is y(pi/2)=1
The solution to the IVP is y=(1-2cosx)^.5
That I know is correct, but they're saying the interval of existence is when pi/3<x<5*pi/3.
Is that wrong? I think it should include the π/3 and 5π/3.
 
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  • #2
No, y=0 at the endpoints. Look at what that does to your original equation.
 

What is a differential equation?

A differential equation is a mathematical equation that relates an unknown function to its derivatives.

What is an interval of existence in a differential equation?

An interval of existence in a differential equation is the range of values for which a solution to the equation exists. It is typically expressed as a range of values for the independent variable.

How do you determine the interval of existence for a differential equation?

The interval of existence for a differential equation can be determined by analyzing the coefficients and initial conditions of the equation, as well as any restrictions on the independent variable.

Why is the interval of existence important in differential equations?

The interval of existence is important because it tells us the range of values for which a solution to the equation exists. This information can help us determine the feasibility of the solution and make predictions about the behavior of the system described by the equation.

What happens if the interval of existence for a differential equation is infinite?

If the interval of existence is infinite, it means that the solution to the equation exists for all values of the independent variable. This is often the case for simple differential equations with no restrictions on the independent variable.

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