Advanced Search

Question: Can Maple dsolve obtain this AI solution to this first order ode?

Question:Can Maple dsolve obtain this AI solution to this first order ode?

nm 12283 Maple 2026
differential-equations
1 hour ago
0

Any one knows a trick to help Maple obtain this much simpler solution to this ode obtained using AI?

ode := 4*(-1 + sqrt(1 - 1/x^2)*x^2)*sec(4 + 4*x + 4*arccsc(x))^2 - sqrt(1 - 1/x^2)*x^2*diff(f(x), x) = 0


 

> 

ode:= 4*(-1 + sqrt(1 - 1/x^2)*x^2)*sec(4 + 4*x + 4*arccsc(x))^2 - sqrt(1 - 1/x^2)*x^2*diff(f(x), x) = 0;

4*(-1+(1-1/x^2)^(1/2)*x^2)*sec(4+4*x+4*arccsc(x))^2-(1-1/x^2)^(1/2)*x^2*(diff(f(x), x)) = 0

> 

maple_sol:=dsolve(ode);

f(x) = c__1+Int(8*(-1+(1-1/x^2)^(1/2)*x^2)*x^6/((1-1/x^2)^(1/2)*(-8*((x^2-1)/x^2)^(1/2)*x^7*sin(8+8*x)+x^8*cos(8+8*x)+x^8+80*((x^2-1)/x^2)^(1/2)*x^5*sin(8+8*x)-32*x^6*cos(8+8*x)-192*((x^2-1)/x^2)^(1/2)*x^3*sin(8+8*x)+160*x^4*cos(8+8*x)+128*((x^2-1)/x^2)^(1/2)*x*sin(8+8*x)-256*cos(8+8*x)*x^2+128*cos(8+8*x))), x)

> 

odetest(maple_sol,ode);

0

> 

AI_sol:=f(x)=_C1+tan(4*(1+x+arccsc(x)));

f(x) = c__1+tan(4+4*x+4*arccsc(x))

> 

odetest(AI_sol,ode)

0

> 

 


 

Download AI_sol.mw
Please Wait...