# Questions tagged [initial-value-problems]

This tag is about questions regarding Initial value problems. In the field of differential equations, an initial value problem is an ordinary differential equation together with a specified value, called the initial condition, of the unknown function at a given point in the domain of the solution.

858 questions
Filter by
Sorted by
Tagged with
19 views

44 views

### Laplace transforms and IVP solutions

When deriving the Laplace transform, we note that the Laplace transform of a function is only defined for $x\ge 0$ (unless in the bilateral case you set $f(x)=0$ for $x \lt 0$). However, we often ...
17 views

### Maximal Interval of Existence for a particular System of Differential Equations

Consider \begin{align} x' &= (x^2+y^2)\sqrt{|y|}\\ y' &= \frac{1}{y^{42}+1}+\exp(t) \end{align} and let $J \subseteq \mathbb{R}$ denote the maximal interval of existence for the solution ...
23 views

### Largest interval of validity for the solution of a first-order DE.

I have been trying to solve for the largest interval for which the particular solution of the differential equation \begin{equation*} 9x^2 \frac{dy}{dx} = y^2+3xy-36x^2, \; \; y(-1) = 0 \end{equation*}...
70 views

24 views

84 views

### Properties of the Solutions of $y' = y$

In this section of my notes we take $E(x)$ as a solution of the initial value problem $y'=y , y(0)= 1$ We show that $E(x+r)$ is also a solution to this problem and show $E(x+r)=E(x)E(r)$. The notes ...
29 views

### Hyperbolastic rate equation of type II already has its initial condition in it?

I'm modelling some real-world gene expression data with various growth models including linear, exponential, and Verhulst growth but not all of the genes are showing these forms of time-dependence. ...
18 views

### Square shape initial condition in MATLAB

I am analyzing $1$D convection equation in MATLAB using Finite Difference method I would like to start the concentration $C(x,t)$ with a square pulse, and see how this square moves in space and time. ...
31 views