Help me - A function satisfies the differential equation

• butbi9x
In summary, the conversation discusses a function that satisfies the differential equation dy/dt = y^4 - 6y^3 + 5y^2. It asks for the constant solutions of the equation and for what values of y the function is increasing and decreasing. The speaker also suggests not to solve the differential equation, but rather an algebraic equation and two inequalities. They also provide a suggestion for solving the problem.
butbi9x
A function satisfies the differential equation:

$$\frac{dy}{dt}= y^{4}-6y^{3}+5y^{2}$$

a. What are the constant solutions of the equation?
b. For what values of y is y increasing?
c. For what values of y is y decreasing?

What are your thoughts on the problem? What have you attempted thus far?

dy/dt=y'(t), its ur function or, simple, y(t), after integration.

Last edited:
butbi9x said:
A function satisfies the differential equation:

$$\frac{dy}{dt}= y^{4}-6y^{3}+5y^{2}$$

a. What are the constant solutions of the equation?
b. For what values of y is y increasing?
c. For what values of y is y decreasing?
Do you understand that this does NOT require that you actually solve the differential equation? It only requires that you solve an algebraic equation and two inequalities.

i think it should be
y'(t)=t^4-6t^3+5t^2
where
y'(t)=dy/dt
now integrate it
we have
y(t)=...
constant solution mean y'(t)=0.
mean no variation w.r.t "t".
for what value of "t" is y increasing...
and for what value of "t" is y decreasing.
i think now u can handle it easily

Last edited:
masqau said:
i think it should be
y'(t)=t^4-6t^3+5t^2
No, that's completely wrong. The DE equation is dy/dt = y4 - 6y3 + 5y2. If if were as you have it, this would be a different problem completely.
masqau said:
where
y'(t)=dy/dt
now integrate it
we have
y(t)=...
constant solution mean y'(t)=0.
mean no variation w.r.t "t".
for what value of "t" is y increasing...
and for what value of "t" is y decreasing.
i think now u can handle it easily

1. What is a differential equation?

A differential equation is a mathematical equation that relates a function with its derivatives. It describes how a quantity changes over time or space, and it is often used to model physical phenomena in science and engineering.

2. How do you know if a function satisfies a differential equation?

A function satisfies a differential equation if it satisfies the equation when its derivatives are substituted into it. This means that when the function and its derivatives are plugged into the equation, the equation is true.

3. What does it mean for a function to be a solution to a differential equation?

A solution to a differential equation is a function that satisfies the equation. This means that the function, when plugged into the equation, makes the equation true. A solution can also be thought of as a curve or a set of curves that satisfies the equation.

4. How are differential equations used in science?

Differential equations are used in science to model and understand various physical phenomena. They are used in fields such as physics, chemistry, biology, and engineering to describe how quantities change over time or space. They can also be used to make predictions and solve problems in these fields.

5. What are some common techniques used to solve differential equations?

There are several techniques used to solve differential equations, including separation of variables, substitution, and integrating factors. Other methods include using series or Laplace transforms, as well as numerical methods such as Euler's method or Runge-Kutta methods.

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