# Initial Value Problem. I'm really confused just need some help

• mazz1801
In summary, the initial value problem (dx/dt)-xt=-t with x(0)=2 can be solved by integrating both sides to get ln[x-1] + C = (1/2)t^2. By substituting t=1 and solving for x, we can determine the value of x(1).
mazz1801

## Homework Statement

Solve the following Initial Value problem for x(t) and give the value of x(1)

## Homework Equations

(dx/dt)-xt=-t , x(0)=2

## The Attempt at a Solution

(dx/dt)-xt = -t
(dx/dt) = xt-t
(dx/dt) = t(x-1)
(1/(x-1)) (dx/dt) = t
(1/(x-1)) dx = t dt

Then I integrate both sides.

∫(1/(x-1)) dx = ∫t dt
ln[x-1] + C = (1/2)t^2

I put x=2 and t=0
ln[1] + C = (1/2)(0)^2
0 + C = 0
C = 0

So my problem is the x(1) bit... I don't know where to go with this... would I just make t=1 and solve for x and give a numerical answer by subbing i back in?
Or am I way of the mark and have everything wrong :O

welcome to pf!

hi mazz1801! welcome to pf!

(try using the X2 button just above the Reply box )
mazz1801 said:
ln[x-1] + C = (1/2)t^2

C = 0

So my problem is the x(1) bit... I don't know where to go with this... would I just make t=1 and solve for x and give a numerical answer by subbing i back in?

("subbing i"? )

yes, that's fine

you should now get rid of the ln by writing x-1 = et2/2

then put t = 1

Thank you very much tiny-tim :)

## 1. What is an Initial Value Problem (IVP)?

An Initial Value Problem is a mathematical problem that involves finding a function or set of functions that satisfies a given set of conditions. These conditions usually include an initial value for the function and a differential equation that describes the behavior of the function.

## 2. How is an IVP different from other mathematical problems?

The main difference between an Initial Value Problem and other mathematical problems is that it involves finding a specific function or set of functions that satisfy a given set of conditions, rather than finding a general solution or solving for a variable.

## 3. What are some real-life applications of IVPs?

Initial Value Problems are commonly used in physics, engineering, and other scientific fields to model and solve real-world problems. For example, they can be used to predict the motion of a projectile, the growth of a population, or the spread of a disease.

## 4. How do you solve an IVP?

There are various methods for solving Initial Value Problems, depending on the complexity of the problem and the type of differential equation involved. Some common techniques include separation of variables, substitution, and using mathematical software or algorithms.

## 5. What are some tips for solving an IVP?

Some tips for solving Initial Value Problems include carefully reading and understanding the given conditions, using appropriate mathematical techniques, and double-checking your solution for accuracy. It may also be helpful to break the problem into smaller, more manageable steps.

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