# 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 $$y'+xy=1+x; \text{ } y(3/2)=0$$ I am able to solve the non homogeneous linear differential equation to find: 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 ...
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### Solving a Cauchy problem

Given the equation $$y' = e^t \sqrt[3]{y^2}$$ (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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