# Questions tagged [cauchy-problem]

Use this tag for questions about partial differential equations that satisfy certain conditions given on a hypersurface in the domain.

53 questions
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### How to solve the Cauchy problem $y'+xy=1+x$; $y(3/2)=0$

Given \begin{equation} y'+xy=1+x; \text{ } y(3/2)=0 \end{equation} I am able to solve the non homogeneous linear differential equation to find: \begin{equation} y=e^{-\frac{x^{2}}{2}}(\int e^{\...
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### Solving a Cauchy Problem using Method of Characteristics

I came across a partial differential equation (IVP PDE) that I would like to solve: $$\{u_y+cos(ky)u_x=ax^2 | u(x,0)=0\}$$ This should be a quasilinear PDE, and is in the format of a Cauchy ...
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### Local uniqueness of solution for quasi linear PDE

I've a little troubles in proving local uniqueness of solution for Cauchy problems concerning quasilinear PDE's. It's a little bit boring, but I tried to be as clear as possible. Suppose $\Omega$ is ...
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### Cauchy simulation in R

How do I simulate Cauchy distribution from Uniform distribution in (-pi/2, pi/2) in R? Not allowed to used any functions that already exist in R that generate Cauchy
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### Computation of a wave equation using Kirchoff's formula !!

I want to solve this wave equation in $3$-D using Kirchoff's formula but all I've done it doesn't work. In particular I'm not able to compute the integral in Kirchoff's formula. you can see the ...
0answers
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### Solving a Cauchy problem

Given the equation $$y' = e^t \sqrt{y^2}$$ (a) consider the related Cauchy problem with $y(t_0)=y_0$. What $P(t_0,y_0)$ ensures the problem has a unic solution? (b) find the general integral of ...
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### Difference between weak and strong formulation of a Cauchy problem solution

While studying the theory of differential equations (only ordinary equations in fact, I'm just getting started), the teacher told us about these two different kinds of formulation. Given a Cauchy ...