Differential Equations
posted by Erica .
For the following initial value problem:
dy/dt=1/((y+1)(t2))
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(2lnt2+C)1 and I don't really know where to go from there.

y = √(2lnt2+C)1
we know that √x is defined only for x >= 0, so we must have
2lnt2 + C >= 0
lnt2 >= C/2
t2 >= e^(C/2)
t >= 2+e^(C/2)
In general, t>=2, but the form of the solution suggested that already.
As t > 2, lnt2 > 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.
Respond to this Question
Similar Questions

Differential Equations (Another) Cont.
For the following initial value problem: dy/dt=1/((y+1)(t2)) 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 … 
Differential Equations
For the following initial value problem: dy/dt=1/((y+1)(t2)), y(0)=0 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 … 
Differential Equations
a) Sketch the phase line for the differential equation dy/dt=1/((y2)(y+1)) and discuss the behavior of the solution with initial condition y(0)=1/2 b) Apply analytic techniques to the initialvalue problem dy/dt=1/((y2)(y+1))), y(0)=1/2 … 
Differental Equations
a) Sketch the phase line for the differential equation dy/dt=1/((y2)(y+1)) and discuss the behavior of the solution with initial condition y(0)=1/2 b) Apply analytic techniques to the initialvalue problem dy/dt=1/((y2)(y+1))), y(0)=1/2 … 
Differential Equations
a) Sketch the phase line for the differential equation dy/dt=1/((y2)(y+1)) and discuss the behavior of the solution with initial condition y(0)=1/2 b) Apply analytic techniques to the initialvalue problem dy/dt=1/((y2)(y+1))), y(0)=1/2 … 
calculus
(A) Consider the wave equation with c=1, l=1, u(0,t)=0, and u(l,t)=0. The initial data are: f(x)=x(1x)2, g(x)=sin2(pi x). Find the value of the solution at x=0, t=10, and at x=1/3, t=0. Find the value of the solution at x=1/2, t=2. … 
Math: Differential Equations
Solve the initial value problem y' = y^2, y(0) = 1 and determine the interval where the solution exists. I understand how the final solution comes to y = 1/(1x), but do not understand how the solution is defined from (infinity, 1) … 
calculus
Find the domain for the particular solution to the differential equation dx/dy=1/2x, with initial condition y(1) = 1. 
calculus
Find the domain for the particular solution to the differential equation dy dx equals the quotient of 3 times y and x, with initial condition y(1) = 1. 
Differential equations,Calculus
So I have the following differential equation. The general solution I have is: t=k(1/r)+c I now need to find the particular solution when t=0 and the radius (r) = 1cm. So k is a constant which is approx 3.9 (5/4pi) So for the particular …