# Solve IVP 2000 #23: Y(0)=A Solution

• MHB
• karush
In summary, "Solve IVP 2000 #23" refers to a problem from the International Physics Olympiad (IPO) 2000 competition, in which participants were asked to solve an Initial Value Problem (IVP) labeled as #23. This involves using given conditions or equations to find a solution for a specific variable or set of variables. In this context, Y(0)=A is an initial condition that means at the starting point of the problem, the variable Y has a value of A. The specific steps for solving the IVP 2000 #23 problem will vary, but generally involve understanding the problem, manipulating equations, and checking the solution. Solving IVP problems is important in physics because it allows
karush
Gold Member
MHB
2000
given #23

so far

I could not get to the W|A solution before applying the y(0)=ahere is the book answer for the rest

Last edited:
$e^{-2t/3} y' - \dfrac{2e^{-2t/3}}{3} y = \dfrac{1}{3}e^{-(3\pi+4)t/6}$

$\left(e^{-2t/3} y \right)' = \dfrac{1}{3}e^{-(3\pi+4)t/6}$

$e^{-2t/3} y = -\dfrac{2}{3\pi+4}e^{-(3\pi+4)t/6} + C$

$y = Ce^{2t/3} -\dfrac{2}{3\pi+4}e^{-\pi t/2}$

mahalo
noticed there was 430+ views on this one

## 1. What is an IVP?

An IVP, or initial value problem, is a type of differential equation that involves finding a function that satisfies both a given differential equation and a set of initial conditions. In other words, the solution must pass through a specific point on the graph.

## 2. What does Y(0)=A mean in this context?

In this context, Y(0)=A represents the initial condition of the IVP. It means that when the independent variable (usually denoted by t) is equal to 0, the dependent variable (usually denoted by y) has a value of A.

## 3. What is the solution to IVP 2000 #23?

The solution to IVP 2000 #23 is a function that satisfies the given differential equation and initial condition. It can be found by using various methods, such as separation of variables, substitution, or using an integrating factor.

## 4. How do you solve an IVP?

To solve an IVP, you must first identify the given differential equation and initial condition. Then, you can use various methods, such as separation of variables, substitution, or using an integrating factor, to find the solution. It is important to check that the solution satisfies both the differential equation and the initial condition.

## 5. What is the significance of the number 2000 in IVP 2000 #23?

The number 2000 in IVP 2000 #23 represents the year in which the problem was published or assigned. It is used to differentiate this specific IVP from others that may have the same number but were published in different years. This numbering system is often used in textbooks and exams to organize and categorize problems.

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