I am modelling the nonlinear behaviour of a sausage in hot water. I am trying to explain it's rotational, vibrational and translational motion in water with salt and subject to varying temperatures. I got the following equation. How do I solve the following equation analytically? $$x^2\frac{∂^4x}{∂y^4}+\frac32\frac{∂^2x}{∂y^2}+x\frac{∂x}{∂z}-\frac{Ax}{\frac{∂^3x}{∂z^3}}=B$$ Where $x=x(z,y)$ and $A$ and $B$ are constants. I would also appreciate if the graph is provided. $$x(0)= {e^3}$$
2026-03-30 11:03:30.1774868610
Solving a fourth order non linear differential equation for explaining motion of a sausage in hot water.
96 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in REAL-ANALYSIS
- how is my proof on equinumerous sets
- Finding radius of convergence $\sum _{n=0}^{}(2+(-1)^n)^nz^n$
- Optimization - If the sum of objective functions are similar, will sum of argmax's be similar
- On sufficient condition for pre-compactness "in measure"(i.e. in Young measure space)
- Justify an approximation of $\sum_{n=1}^\infty G_n/\binom{\frac{n}{2}+\frac{1}{2}}{\frac{n}{2}}$, where $G_n$ denotes the Gregory coefficients
- Calculating the radius of convergence for $\sum _{n=1}^{\infty}\frac{\left(\sqrt{ n^2+n}-\sqrt{n^2+1}\right)^n}{n^2}z^n$
- Is this relating to continuous functions conjecture correct?
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Absolutely continuous functions are dense in $L^1$
- A particular exercise on convergence of recursive sequence
Related 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 GRAPHING-FUNCTIONS
- Lower bound of bounded functions.
- Do Irrational Conjugates always come in pairs?
- Graph rotation: explanation of equation
- Plot function y = tan(yx)
- Sketching a lemniscate curve with a max function?
- 3 points on a graph
- show $f(x)=f^{-1}(x)=x-\ln(e^x-1)$
- What is this method of sketching a third degree curve?
- Getting a sense of $f(x) = x (\log x)^6$
- Can I describe an arbitrary graph?
Related Questions in NONLINEAR-SYSTEM
- Solving special (simple?) system of polynomial equations (only up to second degree)
- Determination of Invertibility
- Question about stability of a nonlinear dynamical system
- The equation $x^T A x = (x^2)^T A x^2$
- 1D viscous flow upwards against gravity
- Convergence of fixed-point in a gauss-seidel style
- Intuition behind dense orbits
- Determine the stability properties and convergence in the origin using Lyapunov Direct Method
- Is $x(t/2)$ a causal/memoryless system?
- Why this field with non-zero curl has closed orbit?
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?