how to solve this set of integro-differential equations analytically?
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I'm stuck with the following system of integro-differential equations and I need to know if it can be analytically solved or not.
$$dot{f}(x)+ a_1 f(x) + a_2int_{x_0}^x k(x,y) f(y) dy+a_3= b_1 g(x)+b_2 int_{x_0}^x k(x,y) g(y) dy $$
$$dot{g}(x)+ c_1 g(x) +c_2 int_{x_0}^x k(x,y) g(y) dy+c_3= d_1 f(x)+ d_2int_{x_0}^x k(x,y) f(y) dy$$
Excluding $f$ and $g$, all function and coefficients are known.
Please let me know if you have any idea for solving this or any clue to better search for the answer.
integration
asked Dec 25 '18 at 10:51
Saeideh EsfandiarpourSaeideh Esfandiarpour
62
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add a comment |
$begingroup$
I'm stuck with the following system of integro-differential equations and I need to know if it can be analytically solved or not.
$$dot{f}(x)+ a_1 f(x) + a_2int_{x_0}^x k(x,y) f(y) dy+a_3= b_1 g(x)+b_2 int_{x_0}^x k(x,y) g(y) dy $$
$$dot{g}(x)+ c_1 g(x) +c_2 int_{x_0}^x k(x,y) g(y) dy+c_3= d_1 f(x)+ d_2int_{x_0}^x k(x,y) f(y) dy$$
Excluding $f$ and $g$, all function and coefficients are known.
Please let me know if you have any idea for solving this or any clue to better search for the answer.
integration
asked Dec 25 '18 at 10:51
Saeideh EsfandiarpourSaeideh Esfandiarpour
62
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Welcome to MSE. Which equations?
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– José Carlos Santos
Dec 25 '18 at 10:56
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Thank you. The two coupled integro-differential equations that I have added to the question.
$endgroup$
– Saeideh Esfandiarpour
Dec 25 '18 at 11:38
add a comment |
$begingroup$
I'm stuck with the following system of integro-differential equations and I need to know if it can be analytically solved or not.
$$dot{f}(x)+ a_1 f(x) + a_2int_{x_0}^x k(x,y) f(y) dy+a_3= b_1 g(x)+b_2 int_{x_0}^x k(x,y) g(y) dy $$
$$dot{g}(x)+ c_1 g(x) +c_2 int_{x_0}^x k(x,y) g(y) dy+c_3= d_1 f(x)+ d_2int_{x_0}^x k(x,y) f(y) dy$$
Excluding $f$ and $g$, all function and coefficients are known.
Please let me know if you have any idea for solving this or any clue to better search for the answer.
integration
asked Dec 25 '18 at 10:51
Saeideh EsfandiarpourSaeideh Esfandiarpour
62
$endgroup$
I'm stuck with the following system of integro-differential equations and I need to know if it can be analytically solved or not.
$$dot{f}(x)+ a_1 f(x) + a_2int_{x_0}^x k(x,y) f(y) dy+a_3= b_1 g(x)+b_2 int_{x_0}^x k(x,y) g(y) dy $$
$$dot{g}(x)+ c_1 g(x) +c_2 int_{x_0}^x k(x,y) g(y) dy+c_3= d_1 f(x)+ d_2int_{x_0}^x k(x,y) f(y) dy$$
Excluding $f$ and $g$, all function and coefficients are known.
Please let me know if you have any idea for solving this or any clue to better search for the answer.
integration
integration
asked Dec 25 '18 at 10:51
Saeideh EsfandiarpourSaeideh Esfandiarpour
62
asked Dec 25 '18 at 10:51
Saeideh EsfandiarpourSaeideh Esfandiarpour
62
edited Dec 25 '18 at 12:33
Saeideh Esfandiarpour
asked Dec 25 '18 at 10:51
Saeideh EsfandiarpourSaeideh Esfandiarpour
62
asked Dec 25 '18 at 10:51
Saeideh EsfandiarpourSaeideh Esfandiarpour
62
asked Dec 25 '18 at 10:51
Saeideh EsfandiarpourSaeideh Esfandiarpour
62
62
$begingroup$
Welcome to MSE. Which equations?
$endgroup$
– José Carlos Santos
Dec 25 '18 at 10:56
$begingroup$
Thank you. The two coupled integro-differential equations that I have added to the question.
$endgroup$
– Saeideh Esfandiarpour
Dec 25 '18 at 11:38
add a comment |
$begingroup$
Welcome to MSE. Which equations?
$endgroup$
– José Carlos Santos
Dec 25 '18 at 10:56
$begingroup$
Thank you. The two coupled integro-differential equations that I have added to the question.
$endgroup$
– Saeideh Esfandiarpour
Dec 25 '18 at 11:38
$begingroup$
Welcome to MSE. Which equations?
$endgroup$
– José Carlos Santos
Dec 25 '18 at 10:56
$begingroup$
Welcome to MSE. Which equations?
$endgroup$
– José Carlos Santos
Dec 25 '18 at 10:56
$begingroup$
Thank you. The two coupled integro-differential equations that I have added to the question.
$endgroup$
– Saeideh Esfandiarpour
Dec 25 '18 at 11:38
$begingroup$
Thank you. The two coupled integro-differential equations that I have added to the question.
$endgroup$
– Saeideh Esfandiarpour
Dec 25 '18 at 11:38
add a comment |
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$begingroup$
Welcome to MSE. Which equations?
$endgroup$
– José Carlos Santos
Dec 25 '18 at 10:56
$begingroup$
Thank you. The two coupled integro-differential equations that I have added to the question.
$endgroup$
– Saeideh Esfandiarpour
Dec 25 '18 at 11:38