ODE
\[ x^7 y(x)^2 y'(x)^3+\left (1-3 x^6 y(x)^3\right ) y'(x)^2+3 x^5 y(x)^4 y'(x)-x^4 y(x)^5=0 \] ODE Classification
[[_homogeneous, `class G`]]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.229483 (sec), leaf count = 22
\[\left \{\left \{y(x)\to \sqrt [3]{c_1 x^3+c_1{}^{2/3}}\right \}\right \}\]
Maple ✓
cpu = 1.385 (sec), leaf count = 7860
\[\text {Expression too large to display}\] Mathematica raw input
DSolve[-(x^4*y[x]^5) + 3*x^5*y[x]^4*y'[x] + (1 - 3*x^6*y[x]^3)*y'[x]^2 + x^7*y[x]^2*y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1]^(2/3) + x^3*C[1])^(1/3)}}
Maple raw input
dsolve(x^7*y(x)^2*diff(y(x),x)^3+(1-3*x^6*y(x)^3)*diff(y(x),x)^2+3*x^5*y(x)^4*diff(y(x),x)-x^4*y(x)^5 = 0, y(x))
Maple raw output
[y(x) = 1/3*2^(2/3)/x^2, y(x) = 1/3*(-1/2*2^(2/3)-1/2*I*3^(1/2)*2^(2/3))/x^2, y(x) = 1/3*(-1/2*2^(2/3)+1/2*I*3^(1/2)*2^(2/3))/x^2, Int(-1/_a*(6*(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)*_a^6*y(x)^3-24*_a^6*y(x)^3+(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)-2*(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)+4)/(18*(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)*_a^6*y(x)^3-24*_a^6*y(x)^3+(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)-2*(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)+4),_a = _b .. x)+Intat(6*(-108*x^12*_f^6+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)*x^6*_f^2/(18*(-108*x^12*_f^6+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)*x^6*_f^3-24*x^6*_f^3+(-108*x^12*_f^6+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(2/3)-2*(-108*x^12*_f^6+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)+4)-Int(-1/_a*(2/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*_a^6*_f^3*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)+18*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^2-72*_a^6*_f^2+2/3/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)-2/3/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2))/(18*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^3-24*_a^6*_f^3+(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)-2*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)+4)+1/_a*(6*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^3-24*_a^6*_f^3+(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)-2*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)+4)/(18*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^3-24*_a^6*_f^3+(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)-2*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)+4)^2*(6/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*_a^6*_f^3*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)+54*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^2-72*_a^6*_f^2+2/3/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)-2/3/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)),_a = _b .. x),_f = y(x))+_C1 = 0, Int(-1/_a*(24*I*3^(1/2)*_a^6*y(x)^3-12*(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)*_a^6*y(x)^3-24*_a^6*y(x)^3+I*(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)*3^(1/2)+(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)-4*I*3^(1/2)+4*(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)+4)/(24*I*3^(1/2)*_a^6*y(x)^3-36*(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)*_a^6*y(x)^3-24*_a^6*y(x)^3+I*(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)*3^(1/2)+(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)-4*I*3^(1/2)+4*(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)+4),_a = _b .. x)+Intat(-12*(-108*x^12*_f^6+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)*x^6*_f^2/(24*I*3^(1/2)*x^6*_f^3-36*(-108*x^12*_f^6+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)*x^6*_f^3-24*x^6*_f^3+I*(-108*x^12*_f^6+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(2/3)*3^(1/2)+(-108*x^12*_f^6+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(2/3)-4*I*3^(1/2)+4*(-108*x^12*_f^6+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)+4)-Int(-1/_a*(72*I*3^(1/2)*_a^6*_f^2-4/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*_a^6*_f^3*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)-36*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^2-72*_a^6*_f^2+2/3*I/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*3^(1/2)*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)+2/3/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)+4/3/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2))/(24*I*3^(1/2)*_a^6*_f^3-36*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^3-24*_a^6*_f^3+I*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*3^(1/2)+(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)-4*I*3^(1/2)+4*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)+4)+1/_a*(24*I*3^(1/2)*_a^6*_f^3-12*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^3-24*_a^6*_f^3+I*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*3^(1/2)+(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)-4*I*3^(1/2)+4*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)+4)/(24*I*3^(1/2)*_a^6*_f^3-36*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^3-24*_a^6*_f^3+I*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*3^(1/2)+(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)-4*I*3^(1/2)+4*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)+4)^2*(72*I*3^(1/2)*_a^6*_f^2-12/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*_a^6*_f^3*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)-108*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^2-72*_a^6*_f^2+2/3*I/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*3^(1/2)*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)+2/3/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)+4/3/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)),_a = _b .. x),_f = y(x))+_C1 = 0, Int(-1/_a*(24*I*3^(1/2)*_a^6*y(x)^3+12*(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)*_a^6*y(x)^3+24*_a^6*y(x)^3+I*(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)*3^(1/2)-(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)-4*I*3^(1/2)-4*(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)-4)/(24*I*3^(1/2)*_a^6*y(x)^3+36*(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)*_a^6*y(x)^3+24*_a^6*y(x)^3+I*(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)*3^(1/2)-(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)-4*I*3^(1/2)-4*(-108*_a^12*y(x)^6+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)-4),_a = _b .. x)+Intat(12*(-108*x^12*_f^6+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)*x^6*_f^2/(24*I*3^(1/2)*x^6*_f^3+36*(-108*x^12*_f^6+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)*x^6*_f^3+24*x^6*_f^3+I*(-108*x^12*_f^6+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(2/3)*3^(1/2)-(-108*x^12*_f^6+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(2/3)-4*I*3^(1/2)-4*(-108*x^12*_f^6+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)-4)-Int(-1/_a*(72*I*3^(1/2)*_a^6*_f^2+4/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*_a^6*_f^3*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)+36*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^2+72*_a^6*_f^2+2/3*I/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*3^(1/2)*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)-2/3/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)-4/3/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2))/(24*I*3^(1/2)*_a^6*_f^3+36*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^3+24*_a^6*_f^3+I*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*3^(1/2)-(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)-4*I*3^(1/2)-4*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)-4)+1/_a*(24*I*3^(1/2)*_a^6*_f^3+12*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^3+24*_a^6*_f^3+I*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*3^(1/2)-(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)-4*I*3^(1/2)-4*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)-4)/(24*I*3^(1/2)*_a^6*_f^3+36*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^3+24*_a^6*_f^3+I*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*3^(1/2)-(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)-4*I*3^(1/2)-4*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)-4)^2*(72*I*3^(1/2)*_a^6*_f^2+12/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*_a^6*_f^3*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)+108*(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^2+72*_a^6*_f^2+2/3*I/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*3^(1/2)*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)-2/3/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)-4/3/(-108*_a^12*_f^6+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*(-648*_a^12*_f^5+6*3^(1/2)/(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9*(-1/_f^2*(27*_a^6*_f^3-4)+81*_f*_a^6)+60*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^4*_a^9+216*_a^6*_f^2)),_a = _b .. x),_f = y(x))+_C1 = 0]