Posted by **Erica** on Thursday, January 31, 2013 at 1:12am.

For the following initial value problem:

dy/dt=1/((y+1)(t-2))

a)Find a formula for the solution.

b) State the domain of definition of the solution.

c) Describe what happens to the solution as it approaches the limit of its domain of definition. Why can't the solution be extended for more time?

I separated and integrated and got y(t)=sqrt(2ln|t-2|+C)-1 and I don't really know where to go from there.

- Differential Equations -
**Steve**, Thursday, January 31, 2013 at 10:20am
y = √(2ln|t-2|+C)-1

we know that √x is defined only for x >= 0, so we must have

2ln|t-2| + C >= 0

ln|t-2| >= -C/2

t-2 >= e^(-C/2)

t >= 2+e^(-C/2)

In general, t>=2, but the form of the solution suggested that already.

As t -> 2, ln|t-2| -> infinity

Not sure why large t cannot be used. May be missing some of the characteristics of the problem.

The initial value conditons will determine C.

## Answer this Question

## Related Questions

- Differential Equations - For the following initial value problem: dy/dt=1/((y+1...
- Differential Equations (Another) Cont. - For the following initial value problem...
- Differential Equations - a) Sketch the phase line for the differential equation ...
- calculus - (A) Consider the wave equation with c=1, l=1, u(0,t)=0, and u(l,t)=0...
- Math: Differential Equations - Solve the initial value problem y' = y^2, y(0) = ...
- Differential Equations - a) Sketch the phase line for the differential equation ...
- Differental Equations - a) Sketch the phase line for the differential equation ...
- Math - Find the specific solution for the following differential equations: a) (...
- Differential eqns - a) Sketch the phase line for the differential equation dy/dt...
- Differential equations in Calculus...plsssss help? - Suppose that represents the...