Solving Integral Equation: x(t) = -8?

Thread starter brusier
Start date Apr 7, 2010
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Integral Integral equation

In summary, an integral equation is a mathematical equation that involves an unknown function within an integral sign. The solution to the equation is the function that satisfies the given integral equation. The method for solving an integral equation depends on the specific equation and the type of integral involved, such as using substitution, integration by parts, or variation of parameters. The purpose of solving an integral equation is to find the unknown function that models real-world phenomena in fields like physics, engineering, and economics. In this integral equation, x(t) represents the unknown function and -8 is a constant value, and the equation is asking for the function x(t) that, when integrated, will result in a constant value of -8. Common mistakes when solving integral equations include

Apr 7, 2010

brusier

Homework Statement

I integrated dx/dt = x^2+(1/81)

Homework Equations

My result; 9(arctan(9x))= t+C needed to be solved for initial condition x(0)=-8
and fit into x(t) = format

The Attempt at a Solution

I cannot figure out why the computer is not accepting my solution:
arctan (9x)= (t-14.012)/9

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Apr 7, 2010

PhysicsMark

Wouldn't that be:

[tex]x(t)=\frac{(tan(\frac{t-14.012}{9}))}{9}[/tex]

Related to Solving Integral Equation: x(t) = -8?

1. What is an integral equation?

An integral equation is a mathematical equation that involves an unknown function within an integral sign. The solution to the equation is the function that satisfies the given integral equation.

2. How do you solve an integral equation?

The method for solving an integral equation depends on the specific equation and the type of integral involved. Some common techniques include using substitution, integration by parts, and the method of variation of parameters.

3. What is the purpose of solving an integral equation?

The purpose of solving an integral equation is to find the unknown function that satisfies the given equation. This can be useful in many scientific fields, such as physics, engineering, and economics, where integral equations are used to model real-world phenomena.

4. What does x(t) = -8 represent in the integral equation?

In this integral equation, x(t) represents the unknown function and -8 is a constant value. The equation is asking for the function x(t) that, when integrated, will result in a constant value of -8.

5. Are there any common mistakes when solving integral equations?

Yes, there are some common mistakes that can occur when solving integral equations. These include incorrect use of integration techniques, missing or incorrect boundary conditions, and errors in algebraic manipulations. It is important to double-check all steps and solutions when solving integral equations.