Question

Is there any other solution to the integral equation $\int_{0}^{\infty}e^{kx}f(x) dx=\frac{k^2+k}{k^3},k<0$ except $f(x)=x-1$?

score 46 · Answer 1 · 2019-07-24 04:32:33

46

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Is there any other solution to the integral equation $\int_{0}^{\infty}e^{kx}f(x) dx=\frac{k^2+k}{k^3},k<0$ except $f(x)=x-1$?

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67

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273

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score 137 · Answer 11 · 2019-09-23 06:22:55

137

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469

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82

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List Question

Is there any other solution to the integral equation $\int_{0}^{\infty}e^{kx}f(x) dx=\frac{k^2+k}{k^3},k<0$ except $f(x)=x-1$?

Solving Equations of operators with the delta function (Example)

Finding decaying solution for a nonlinear ODE

How to find $f(x)$ in the following integral equation?

Generalizing Archimedes' "The Quadrature of the Parabola"

an interesting question related to formulation of a method for reduction of a BVP to an integral equation

reduction of IVP with variable coefficient into Volterra integral equation

Fredholm integral equation of 2. order

Why solving a differentiated integral equation might eventually lead to erroneous solutions of the original problem?

solving the Volterra integral equation $Y(t)=F(t)+\int_0^t (t^2-x^2)Y(x)dx$

Help with unsolved indefinite integral ! $\int \!r\ln \left( r \right) \sqrt {ar+{b}^{2}+{r}^{2}}\,{\rm d}r$

Prove that there exists a unique continuous function $ f:[0,1]\to\mathbb R$ such that $f(x)=\sin x+\int_0^1 f(y)\exp(-x-y-1)dy$

Reading Speed for Constant Time to Finish

Solution of Volterra convolution-type integral equation

Why are mathematician so interested to find theory for solving partial differential equations but not for integral equation?

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