ODE
\[ x^4 y'(x)^3-x^3 y(x) y'(x)^2-x^2 y(x)^2 y'(x)+x y(x)^3=1 \] ODE Classification
[[_1st_order, _with_linear_symmetries]]
Book solution method
Change of variable
Mathematica ✗
cpu = 600.012 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 6.289 (sec), leaf count = 400
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{3}-{\frac {27}{32\,x}}=0,\ln \left ( x \right ) -6\,\int ^{y \left ( x \right ) \sqrt [3]{x}}\!{\frac {\sqrt [3]{-16\,{{\it \_a}}^{3}+3\,\sqrt {-96\,{{\it \_a}}^{3}+81}+27}}{\sqrt [3]{4}\sqrt [3]{ \left ( -16\,{{\it \_a}}^{3}+3\,\sqrt {-96\,{{\it \_a}}^{3}+81}+27 \right ) ^{2}}+8\,\sqrt [3]{2}{{\it \_a}}^{2}+4\,\sqrt [3]{-16\,{{\it \_a}}^{3}+3\,\sqrt {-96\,{{\it \_a}}^{3}+81}+27}{\it \_a}}}{d{\it \_a}}-{\it \_C1}=0,\ln \left ( x \right ) -12\,\int ^{y \left ( x \right ) \sqrt [3]{x}}\!{\frac {\sqrt [3]{-16\,{{\it \_a}}^{3}+3\,\sqrt {-96\,{{\it \_a}}^{3}+81}+27}}{i\sqrt {3}\sqrt [3]{4}\sqrt [3]{ \left ( -16\,{{\it \_a}}^{3}+3\,\sqrt {-96\,{{\it \_a}}^{3}+81}+27 \right ) ^{2}}-8\,i\sqrt [3]{2}\sqrt {3}{{\it \_a}}^{2}-\sqrt [3]{4}\sqrt [3]{ \left ( -16\,{{\it \_a}}^{3}+3\,\sqrt {-96\,{{\it \_a}}^{3}+81}+27 \right ) ^{2}}-8\,\sqrt [3]{2}{{\it \_a}}^{2}+8\,\sqrt [3]{-16\,{{\it \_a}}^{3}+3\,\sqrt {-96\,{{\it \_a}}^{3}+81}+27}{\it \_a}}}{d{\it \_a}}-{\it \_C1}=0,\ln \left ( x \right ) +12\,\int ^{y \left ( x \right ) \sqrt [3]{x}}\!{\frac {\sqrt [3]{-16\,{{\it \_a}}^{3}+3\,\sqrt {-96\,{{\it \_a}}^{3}+81}+27}}{i\sqrt {3}\sqrt [3]{4}\sqrt [3]{ \left ( -16\,{{\it \_a}}^{3}+3\,\sqrt {-96\,{{\it \_a}}^{3}+81}+27 \right ) ^{2}}-8\,i\sqrt [3]{2}\sqrt {3}{{\it \_a}}^{2}+\sqrt [3]{4}\sqrt [3]{ \left ( -16\,{{\it \_a}}^{3}+3\,\sqrt {-96\,{{\it \_a}}^{3}+81}+27 \right ) ^{2}}+8\,\sqrt [3]{2}{{\it \_a}}^{2}-8\,\sqrt [3]{-16\,{{\it \_a}}^{3}+3\,\sqrt {-96\,{{\it \_a}}^{3}+81}+27}{\it \_a}}}{d{\it \_a}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[x*y[x]^3 - x^2*y[x]^2*y'[x] - x^3*y[x]*y'[x]^2 + x^4*y'[x]^3 == 1,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(x^4*diff(y(x),x)^3-x^3*y(x)*diff(y(x),x)^2-x^2*y(x)^2*diff(y(x),x)+x*y(x)^3 = 1, y(x),'implicit')
Maple raw output
y(x)^3-27/32/x = 0, ln(x)-6*Intat((-16*_a^3+3*(-96*_a^3+81)^(1/2)+27)^(1/3)/(4^(1/3)*((-16*_a^3+3*(-96*_a^3+81)^(1/2)+27)^2)^(1/3)+8*2^(1/3)*_a^2+4*(-16*_a^3+3*(-96*_a^3+81)^(1/2)+27)^(1/3)*_a),_a = y(x)*x^(1/3))-_C1 = 0, ln(x)+12*Intat((-16*_a^3+3*(-96*_a^3+81)^(1/2)+27)^(1/3)/(I*3^(1/2)*4^(1/3)*((-16*_a^3+3*(-96*_a^3+81)^(1/2)+27)^2)^(1/3)-8*I*2^(1/3)*3^(1/2)*_a^2+4^(1/3)*((-16*_a^3+3*(-96*_a^3+81)^(1/2)+27)^2)^(1/3)+8*2^(1/3)*_a^2-8*(-16*_a^3+3*(-96*_a^3+81)^(1/2)+27)^(1/3)*_a),_a = y(x)*x^(1/3))-_C1 = 0, ln(x)-12*Intat((-16*_a^3+3*(-96*_a^3+81)^(1/2)+27)^(1/3)/(I*3^(1/2)*4^(1/3)*((-16*_a^3+3*(-96*_a^3+81)^(1/2)+27)^2)^(1/3)-8*I*2^(1/3)*3^(1/2)*_a^2-4^(1/3)*((-16*_a^3+3*(-96*_a^3+81)^(1/2)+27)^2)^(1/3)-8*2^(1/3)*_a^2+8*(-16*_a^3+3*(-96*_a^3+81)^(1/2)+27)^(1/3)*_a),_a = y(x)*x^(1/3))-_C1 = 0