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View Equation

The database contains 327 equations (8 equations are awaiting activation).

Equation data
Category:5. Integral Equations
Subcategory:5.3. Linear Equations of the First Kind with Constant Limits of Integration
Equation(s):$\displaystyle \int^\infty_0[tJ_\nu(xt)+\varphi(x)\psi(t)]y(t)\,dt=f(x)$.
Solution(s),
Transformation(s),
Integral(s)
:
Here $J_\nu(z)$ is the Bessel function of the first kind and $\nu>-1$.

Solution:
$$
y(t)=y_f(t)+Ay_\varphi(t),
$$
where
$$
y_f(t)=\int^{\infty}_0xJ_\nu(xt)f(x)\,dx,\quad
y_\varphi(t)=\int^{\infty}_0xJ_\nu(xt)\varphi(x)\,dx,\quad
A=-\frac{\int^\infty_0\psi(t)y_f(t)\,dt}{1+\int^\infty_0\psi(t)y_\varphi(t)\,dt}.
$$
Novelty:New equation(s) & solution(s) / integral(s)
Author/Contributor's Details
Last name:Polyanin
First name:Andrei
Country:Russia
City:Moscow
Statistic information
Submission date:Mon 09 Jul 2007 12:08
Edits by author:0

Edit (Only for author/contributor)


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