List questions from fundamental-solution

Published on 10 May 2026 - 19:38

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Solving Laplacian in $\mathbb{R}^2$

Published on 25 Mar 2026 - 14:00

224

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General solution of $x^2 u_{xx} - 2xy u_{xy} + y^2 u_{yy} = e^x$

Published on 25 Mar 2026 - 13:55

236

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On the solution of the heat equation using distribution theory

Published on 25 Mar 2026 - 13:55

183

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Fundamental Solution of a heat equation with a drift term

Published on 25 Mar 2026 - 13:59

54

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Exactly one homogeneous differential equation of second order to given fundamental solution

Published on 09 Apr 2026 - 16:07

162

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Finding solution of non-homogeneous ODE when we know the solutions of the homogeneous counterpart

Published on 25 Mar 2026 - 13:56

41

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Is this the fundamental solution?

Published on 25 Mar 2026 - 14:00

84

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Show that $\frac 1{4\pi |x|} e^{-c|x|}$ is a fundamental solution for $-\Delta+c^2$ on $\mathbb R^3$

Published on 25 Mar 2026 - 13:55

71

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Verification of the formula of variation of parameters for ODE

Published on 25 Mar 2026 - 13:57

36

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Show that $\lim_{\tau \to t}\int_\Omega \Phi(x-\xi, t-\tau)u(\xi,\tau)d\xi = u(x,t)$

Published on 25 Mar 2026 - 13:56

45

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Fundamental matrix of $x'= (-1+\frac{3}{2}\cos^2t)x+(1-\frac{3}{2}\sin t\cos t)y,~y'=(-1-\frac{3}{2}\sin t \cos t)x+(-1+\frac{3}{2}\sin^2t) y$

Published on 25 Mar 2026 - 13:58

60

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Fundamental matrix solution remains invertible

Published on 25 Mar 2026 - 13:59

81

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Deriving the fundamental solution to heat equation

Published on 25 Mar 2026 - 13:59

51

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Constant Coefficient Operators: Fundamental solution of Cauchy-Riemann Operator - Folland, Introduction to PDE

Published on 25 Mar 2026 - 13:57

List Question

What is a distinct feature of an ambiguous result

Solving Laplacian in $\mathbb{R}^2$

General solution of $x^2 u_{xx} - 2xy u_{xy} + y^2 u_{yy} = e^x$

On the solution of the heat equation using distribution theory

Fundamental Solution of a heat equation with a drift term

Exactly one homogeneous differential equation of second order to given fundamental solution

Finding solution of non-homogeneous ODE when we know the solutions of the homogeneous counterpart

Is this the fundamental solution?

Show that $\frac 1{4\pi |x|} e^{-c|x|}$ is a fundamental solution for $-\Delta+c^2$ on $\mathbb R^3$

Verification of the formula of variation of parameters for ODE

Show that $\lim_{\tau \to t}\int_\Omega \Phi(x-\xi, t-\tau)u(\xi,\tau)d\xi = u(x,t)$

Fundamental matrix of $x'= (-1+\frac{3}{2}\cos^2t)x+(1-\frac{3}{2}\sin t\cos t)y,~y'=(-1-\frac{3}{2}\sin t \cos t)x+(-1+\frac{3}{2}\sin^2t) y$

Fundamental matrix solution remains invertible

Deriving the fundamental solution to heat equation

Constant Coefficient Operators: Fundamental solution of Cauchy-Riemann Operator - Folland, Introduction to PDE

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