Question: How to solve it by Laplace transform?

How evaluate system of two integral equation by laplace transform ?

 

with(inttrans):

L := laplace((1/2)*x^2+(1/2)*x^3+(1/12)*x^4 = int(u(t)*(-1+x-t)+v(t)*(1+x-t), t = 0 .. x), x, s);

(s^2+3*s+2)/s^5 = laplace(int(u(t)*(-1+x-t)+v(t)*(1+x-t), t = 0 .. x), x, s)

 

(3*s^2-s+2)/s^5 = laplace(int((1+x-t)*u(t)+(-1+x-t)*v(t), t = 0 .. x), x, s)

(1)

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