So I'm trying to find a continuous solution for this equation: $dy/dx+y=f(x)$, $f(x)=1$ if $0<=x<=1$ and $f(x)=-1$ if $x>1$ $y(0)=1$. Now I know that this is a linear equation that I have to solve but I'm not sure how to set up the equation and what type of linear equation this is so I don't know how I would solve this. Also what does it mean to find a continuous solution?
2026-03-28 07:48:24.1774684104
How do I find a continuous solution for this linear equation?
784 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
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 CONTINUITY
- Continuity, preimage of an open set of $\mathbb R^2$
- Define in which points function is continuous
- Continuity of composite functions.
- How are these definitions of continuous relations equivalent?
- Show that f(x) = 2a + 3b is continuous where a and b are constants
- continuous surjective function from $n$-sphere to unit interval
- Two Applications of Schwarz Inequality
- Show that $f$ with $f(\overline{x})=0$ is continuous for every $\overline{x}\in[0,1]$.
- Prove $f(x,y)$ is continuous or not continuous.
- proving continuity claims
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
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?
"To find a continuous solution" means: find a solution $y_1(x)$ for $0\le x\le1$ with the given initial condition $y_1(0)=1$, then find a solution $y_2(x)$ for $x>1$ taking as initial condition the value of $y_1(1)$. The global solution is continuous on $[0,+\infty)$.