Hi All,

Is there any way to solve an integral equation, either analytically or numerically?

Thanks,

Daniel Volinski

1 | initial version |

Hi All,

Is there any way to solve an integral equation, either analytically or numerically?

Thanks,

Daniel Volinski

~~Hi All,~~

Is there any way to solve an integral equation, (where the unknown is a function and the equation involves integrals), either analytically or numerically?

~~Thanks,~~For example, can Sage solve a Volterra equation of the second kind?

~~Daniel Volinski~~That would be an equation like:

```
y(x) == integrate(exp(x-t)*y(t), t, 0, x)
```

and the solution is expected in the form $y(x) = ?$ where the right hand side is a function of $x$ not involving $y$.

Can Sage solve integral equations (where the unknown is a function and the equation involves integrals), either analytically or numerically?

For example, can Sage solve a Volterra equation of the second ~~kind?~~kind?

That would be an equation like:

```
y(x) == integrate(exp(x-t)*y(t), t, 0, x)
```

and the solution is expected in the form $y(x) = ?$ where the right hand side is a function of $x$ not involving $y$.

Can Sage solve ~~integral ~~~~equations~~ equations (where the unknown is a ~~function ~~function
and the equation involves ~~integrals),
~~integrals), either analytically or numerically?

References:

For example, can Sage solve a Volterra equation of the second kind~~?~~

That would be an equation like:, such as

```
y(x) == integrate(exp(x-t)*y(t), t, 0, x)
```

~~and the ~~The solution is expected in the form $y(x) = ~~?$ ~~...$ where the right hand side
is ~~a ~~an explicit function of $x$ not involving $y$.

Notice in the example the function $y$ appears in two places, once in the left hand side and the other inside the integral sign.

I am looking for something like what you see in

i.e., a command that would give the solution once I give the equation.

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