Separable Equation with Condition?

In summary, the conversation discusses solving a separable equation with the additional condition of y(2)=2. The process involves factoring and integrating both sides, with the initial condition used to solve for an arbitrary constant.
  • #1
silicon_hobo
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[SOLVED] Separable Equation with Condition?

Homework Statement


Solve.
http://www.mcp-server.com/~lush/shillmud/int3.71.JPG

Homework Equations



The Attempt at a Solution


I'm not sure how to separate this. Also, since the directions consist of only one word, I'm not sure if y(2)=2 is some kind of hint or an additional condition to be fulfilled. I'm wondering where to go after factoring t out of the top. Thanks.
http://www.mcp-server.com/~lush/shillmud/int3.72.JPG
 
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  • #2
Well after factoring... you separate (hence separable equations!)

[tex]\frac{dy}{y+3} = \frac{t}{t^2+1}dt[/tex]

Then integrate both sides.
y(2) = 2 is an initial condition, not a hint... After solving for y(t) you will have one arbitrary constant, which can be solved for using this condition.
 
  • #3
Wow, that seems almost too easy. Thanks.
 

1. What is a separable equation with condition?

A separable equation with condition is a type of differential equation where the dependent variable and independent variable can be separated into separate functions, with the addition of a condition that must also be satisfied.

2. What is the purpose of adding a condition to a separable equation?

The condition in a separable equation ensures that the solution to the equation satisfies a specific requirement or boundary. This can be helpful in solving real-world problems or providing more accurate solutions.

3. How do you know if an equation is separable with condition?

An equation is separable with condition if it can be written in the form dy/dx = f(x)g(y), where f(x) and g(y) are functions of x and y respectively, and there is an additional condition that must be satisfied.

4. Can you give an example of a separable equation with condition?

One example of a separable equation with condition is the equation dy/dx = x/y, where the condition is that y cannot be equal to 0. This equation can be separated into dy/y = xdx, and then solved using integration techniques.

5. What are the advantages of solving a separable equation with condition?

The main advantage of solving a separable equation with condition is that it allows for more precise solutions to problems. It also allows for the incorporation of real-world constraints or boundary conditions, making the solution more applicable to practical situations.

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