Integral equation Definition and 109 Threads

  1. M

    Solving Integral Equation: Analytical & Numerical Solutions

    hi all, i have the following integral equation to solve: .y......x ./....../ | [1/(c1-c2*y)]dy = | [1/(1-x^2/c3^2)]dx /....../ 0......0 where c1, c2, c3 are constants. Can I solve it analytically? If not, how can i dot to find the function x(y) or y(x)? Otherwise, does it exist an...
  2. C

    Solving an Integral Equation: Where's the Error?

    \int \tan x \cdot dx + \int \tan 2y \cdot dy = 0 I get 1 = C\sqrt{\cos 2y} \cos x My init conditions were y(0) = pi/2 so I end up getting C as \sqrt{-1} but the equation should be -1 = \cos 2y \cos^2 x Where's my error?
  3. N

    Integral of (2x+5) (x^2-3) / x - Moshe

    hi guys, i need help with following eqation. (2x+5) (x^2-3) --------------- << entire equation is divide by x. x i need integral value of this equation. thank you in advance, moshe
  4. E

    Integral equation with kernel K(st)

    Hello i would need help to solve the integral equation with Kernel K(st)...
  5. O

    Integrate Equation: What's Needed?

    what does an equation need so that the equation can be integrated? not all of equation can be integarted right? I was quite confuse if it can be integrated or not whether I found a difficult integration. Thanx
  6. S

    Solving Integral Equation: \phi(s) from y(s)

    I'm interested in studying the following equation, solving for \phi(s) given y(s): \int_0^s \frac{2r}{\sqrt{s^2-r^2}} \phi(r)dr=y(s) or in more standard form: \int_0^s K(s,r)\phi(r)=y(s) This is how I think it should be approached: The kernel,K(s,r) is singular at s=r. Thus, the...
  7. E

    Integral equation of second kind and prime number counting function

    in this postcrpit i would like to say i have fund a second order integral equation (fredholm type) for the prime number counting function in particular for Pi(2^t)/2^2t function being Pi(t) the prime number counting function,teh equation is like this is we call Pi(2^t)/2^2t=g(t) then we have...
  8. E

    Cuasi-exact Integral equation for Pi(x)/x 2

    Cuasi-exact Integral equation for Pi(x)/x**2 I thinks i have solved a cuasi exact integral equation for Pi(x)/x**2 expresing this function in terms of eigenfunctions of a symmetric kernel K(s,t)=nexp(-n**2(s-t)**2+s**2(t+s)/2**(5st)-1 form the usual integral equationfor Pi(x)...
  9. E

    Solving Integral Equation with Eigenfunctions

    i am trying to solve the integral equation g(x)=Int(0,infinite)f(t)st/exp(st)-1)) the Kernel is K(s,t)=st/(exp(st)-1) so K(s,t)=K(t,s) is symmetric..so their eigenfunctions will be orthogonal and their eignevalues real..but i do not kow if f(t) belongs to L**2 so we could i solve it using...
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