Find the value of y0 for which the solution touches, but does not cross, the t-axis. (a computer algebra system is recommended. round your answer to three decimal places.)

Step-by-step explanation:

Assuming the following function:

So we want to find a point a such that:

So if we use this condition we can find the value of t=a that satisfy the equirements:

And we have another initial conidtion

Now we need to solve the differential equation and since is a linear equation we can use the integrating factor, our equation have the following form:

We can calculate the integrating factor like this:

Now we can rewrite the differential equation like this:

And if we integrate both sides we got this:

If we divide both sides by we got this:

And we can use the initial condition and we find the value for C like this:

And then we have our solution given by:

And if we use the other initial condition w can solve the value of

And then that would be our final solution:

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are