Question

How to solve the integral equation $f(x) = \int_0^x f(x-y)k(x,y)dy+g(x)$ for $f(x)$?

score 289 · Answer 1 · 2026-04-29 12:18:28

289

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How to solve the integral equation $f(x) = \int_0^x f(x-y)k(x,y)dy+g(x)$ for $f(x)$?

Published on 29 Apr 2026 - 12:18

score 107 · Answer 2 · 2026-04-29 12:44:04

107

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Solving for $f\left(\sqrt{x^2+z^2}\right)$ given $g(z)=\int_{-\infty}^{+\infty}{\left(f\left(\sqrt{x^2+z^2}\right)\frac{1}{\sqrt{x^2+z^2}}\right)}dx$

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score 132 · Answer 3 · 2026-05-10 12:32:06

132

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score 954 · Answer 4 · 2026-04-29 12:44:20

954

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score 567 · Answer 5 · 2026-04-29 12:44:21

567

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score 75 · Answer 6 · 2026-04-29 12:44:05

75

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score 153 · Answer 7 · 2026-04-20 17:00:11

153

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score 76 · Answer 8 · 2026-04-21 10:00:02

76

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54

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1.3k

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score 125 · Answer 11 · 2026-05-05 04:15:25

125

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score 395 · Answer 12 · 2026-05-10 12:32:38

395

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score 133 · Answer 13 · 2026-05-10 12:34:22

133

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score 72 · Answer 14 · 2026-05-10 12:34:57

72

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score 96 · Answer 15 · 2026-05-10 15:01:47

96

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List Question

How to solve the integral equation $f(x) = \int_0^x f(x-y)k(x,y)dy+g(x)$ for $f(x)$?

Solving for $f\left(\sqrt{x^2+z^2}\right)$ given $g(z)=\int_{-\infty}^{+\infty}{\left(f\left(\sqrt{x^2+z^2}\right)\frac{1}{\sqrt{x^2+z^2}}\right)}dx$

Approximate solutions to nonlinear differential equations using an integral sequence

Solving an integral equation by Fourier transform

Composition of bounded linear operator and an inverse of a linear operator bounded?

Volterra equation of first kind

Solution to a Volterra integral equation

Solution to integral equation involving logarithms

Importance of compact operators for numerical approximation of integral equations?

Can integral equations be paired with linear regression to fit a double Gaussian regression?

Solve $f(x) = \lambda\int_0^\pi(x+y)f(y)\mathrm dy$

Solution of Differential equation as an integral equation

Show that the given map F is a contraction map & find a solution of F, if any.

Fredholm Integral Equation of First Kind with finite limits, 1-D

Cast the homogeneous Volterra equation into a first-order differential equation - Solutions are not the same

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