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I have derived two equations of the following type $\dfrac{\delta A}{\delta x}=a\dfrac{\delta B}{\delta t}-b\dfrac{\delta^3 B}{\delta x^2 \delta t}$$$ \dfrac{\partial A}{\partial x}=a\dfrac{\partial B}{\partial t}-b\dfrac{\partial^3 B}{\partial x^2 \partial t}$$ and $\dfrac{\delta B}{\delta x}=\int _0^l e^{-\lambda|x-x'|}\dfrac{\delta A(x')}{\delta t} dx'$$$ \dfrac{\partial B}{\partial x}=\int _0^l e^{-\lambda|x-x'|}\dfrac{\partial A(x')}{\partial t} dx'$$ Where A$A$ and B$B$ are functions of 'x'$x$ and 't'. x$t$, $x$ and x'$x'$ are any point between 0$0$ and $l$. a, b and $\lambda$$a, b, \lambda$ are constants. 
Is it possible to gettransform these two equations into a single partial differential equation on B alone from these equationsfor $B$?

I have derived two equations of the following type $\dfrac{\delta A}{\delta x}=a\dfrac{\delta B}{\delta t}-b\dfrac{\delta^3 B}{\delta x^2 \delta t}$ and $\dfrac{\delta B}{\delta x}=\int _0^l e^{-\lambda|x-x'|}\dfrac{\delta A(x')}{\delta t} dx'$ Where A and B are functions of 'x' and 't'. x and x' are any point between 0 and $l$. a, b and $\lambda$ are constants. Is it possible to get a partial differential equation on B alone from these equations

I have derived two equations of the following type $$ \dfrac{\partial A}{\partial x}=a\dfrac{\partial B}{\partial t}-b\dfrac{\partial^3 B}{\partial x^2 \partial t}$$ and $$ \dfrac{\partial B}{\partial x}=\int _0^l e^{-\lambda|x-x'|}\dfrac{\partial A(x')}{\partial t} dx'$$ Where $A$ and $B$ are functions of $x$ and $t$, $x$ and $x'$ are any point between $0$ and $l$ and $a, b, \lambda$ are constants. 
Is it possible to transform these two equations into a single partial differential equation for $B$?

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user141209
user141209

Coupled partial differential and integro-differential equation

I have derived two equations of the following type $\dfrac{\delta A}{\delta x}=a\dfrac{\delta B}{\delta t}-b\dfrac{\delta^3 B}{\delta x^2 \delta t}$ and $\dfrac{\delta B}{\delta x}=\int _0^l e^{-\lambda|x-x'|}\dfrac{\delta A(x')}{\delta t} dx'$ Where A and B are functions of 'x' and 't'. x and x' are any point between 0 and $l$. a, b and $\lambda$ are constants. Is it possible to get a partial differential equation on B alone from these equations