Is there anyway to solve this differential equation in maple?
(diff(x^2, x))*(diff(w(x), x))/x^2 = 480*(Int(0.2538690379e-2*l^2/(exp(4.651162791*10^6*l^2+9.302325581*10^6*w(x)-1.600000000*10^9)+1), l = 0. .. infinity)); Initial conditions: w(0) at 0 and w'(0)=0.
here's an expression that I am working on.
.014*(Int(r^2*Li[3/2](-exp(x-a(r)))), r = 0 .. 2)) which should be equal to a positive number say 1,
where a(r) is a always negative and x can be any real number (positive or negative). I am writing Li[3/2](-exp(x-a(r))) equal to polylog(3/2,-exp(x-a(r)).
Whatever values I plug in for x and a(r), the left hand side of my equation is always negative. But it should be a positive number.
Would someone mind helping me out with this.