There is an initial value problem where $\frac{dN}{dt}=rN(1-\frac{N}{k}), N(0)=N_0$. I recognize this to be a logistic growth problem. I want to determine the dimensions of $r$ and nondimensionalize the equation. I know that the variavles are $N$ and $t$, so I should substitute a new variable for it to nondimensionalize right? What do I do next here?
2026-03-27 15:35:30.1774625730
Nondimensionalize this equation and find the constant
109 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ORDINARY-DIFFERENTIAL-EQUATIONS
- The Runge-Kutta method for a system of equations
- Analytical solution of a nonlinear ordinary differential equation
- Stability of system of ordinary nonlinear differential equations
- Maximal interval of existence of the IVP
- Power series solution of $y''+e^xy' - y=0$
- Change of variables in a differential equation
- Dimension of solution space of homogeneous differential equation, proof
- Solve the initial value problem $x^2y'+y(x-y)=0$
- Stability of system of parameters $\kappa, \lambda$ when there is a zero eigenvalue
- Derive an equation with Faraday's law
Related Questions in INITIAL-VALUE-PROBLEMS
- Solve $U_{tt}=a U_{xx}$ when a<0.
- Solving $y''+\dfrac{\varepsilon y'}{y^2} - y' = 0, \, y(-\infty)=1$ and $y(\infty) = \varepsilon$
- Solve $u_t+3uu_x=0$ , $u(x,0)=\left\{\begin{matrix} 2 & x<1\\ 0& x>1 \end{matrix}\right.$
- Imposing a condition that is not boundary or initial in the 1D heat equation
- Solve the initial value problem (ODE) and determine how the interval on which its solution exists depends on the initial value?
- The IVP $\begin{cases}\dot{x}=x^3+e^{-t^2}\\x(0)=1\end{cases}$ possesses a solution in $I=(-1/9,1/9)$
- Prove that an IVP with discontinuous $f(t,x)$ has a solution for all $(t_0,x_0)$
- Let $\dot{x}=\arctan(x(t)\cdot t)$, $x(t_0)=x_0$ be an IVP. Prove that if $x_0<0$, then $x(t)<0$ for all $\mathbb{R}$
- Continuity of solutions of an ODE with respect to initial conditions: example
- Differentiable dependence on initial conditions and parameters of an ODE
Related Questions in DIMENSIONAL-ANALYSIS
- Why are radians dimensionless?
- Why the objective function in optimization does not follow dimensional rule?
- Are one-dimensional maps still called the same if they involve multiple functions instead of one recurrent function?
- Finding the maxima of a given function
- Does the absolute value operator pick up dimension?
- Can a one-dimensional shape have volume?
- Units of parameters in differential equation
- Reducing the number of parameters of an ODE system through nondimensionalization
- Can the dimension of a space or quantity be complex?
- Second derivative of $\phi$ in nondimensionalization problem.
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?