Advanced Search

Question: How does Maple solve, int(y'(x)*f(x), x) =[int(sqrt(y(x)) *f(x),x]^(-2/3) ?

Question:How does Maple solve, int(y'(x)*f(x), x) =[int(sqrt(y(x)) *f(x),x]^(-2/3) ?

Joseph Poveromo 25 Maple 2022
ode dsolve differential-equations integro-differential-equation
June 21 2024
0

'odeadvisor' suggests isolating y(x) from the equation as a first step, y=G(x,y'(x)), then apply the method of 'patterns'. For the first step, y(x) = (9/4)*[(y'(x))^2]/{[int(f(x),x)]^5} is what I found but, could take it no further. Nevertheless, Maple finds an intrinsic solution of the form, (3/4)*y(x)^(4/3) +(2/3)*int(sqrt(y(x)*f(x))^(-5/3) + _C1 =0, from which an explicit solution can be obtained. If anyone can supply the steps leading to the Maple solution - that would be great.
Please Wait...