A Differential Equation. NEED your help

[billmmmm]

Hi everyone, I need your help. I am getting trouble in two differential Equation.

The first one:
How can I solve the family of Differential Equation y' = -y*(y-6)^2 - a ? I want to sketch the bifurcation diagram, and what value can “a” be? THX.

The second one:
A DE y' = (1/t)*(2*y + 1). Does there exist a unique solution that satisfies y(-1) = 0? If so, find it. If not, find all solutions and explain why this does not contradict the uniqueness Theorem. How to solve it? Plz.
I am now waiting the answers online. Thx.

 

[Mark44]

Hi everyone, I need your help. I am getting trouble in two differential Equation.

The first one:
How can I solve the family of Differential Equation y' = -y*(y-6)^2 - a ? I want to sketch the bifurcation diagram, and what value can “a” be? THX.

The second one:
A DE y' = (1/t)*(2*y + 1). Does there exist a unique solution that satisfies y(-1) = 0? If so, find it. If not, find all solutions and explain why this does not contradict the uniqueness Theorem. How to solve it? Plz.
I am now waiting the answers online. Thx.

What have you tried? Per the rules of this forum, you need to show some effort at the solution of homework problems.

 

[billmmmm]

What have you tried? Per the rules of this forum, you need to show some effort at the solution of homework problems.

The second one, i think, there is only one solution.

 

[Redbelly98]

Moderator's note: thread moved to Homework forums from Differential Equations.

The second one, i think, there is only one solution.

If you don't explain how you figured that out, people could assume you are just doing a random guess, which really isn't making an attempt at solving the problem.