ODE
\[ 2 y(x) y'(x)^3+3 y(x) y'(x)+x=0 \] ODE Classification
[[_homogeneous, `class A`], _dAlembert]
Book solution method
No Missing Variables ODE, Solve for \(x\)
Mathematica ✗
cpu = 600.001 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.094 (sec), leaf count = 455
\[ \left \{ {\frac {{x}^{2}}{2}}+ \left ( y \left ( x \right ) \right ) ^{2}=0,\ln \left ( x \right ) -\int ^{{\frac {y \left ( x \right ) }{x}}}\!{\frac {1}{2\,{{\it \_a}}^{4}+3\,{{\it \_a}}^{2}+1} \left ( -2\,{{\it \_a}}^{3}-{{{\it \_a}}^{2}{\frac {1}{\sqrt [3]{{{\it \_a} \left ( 2\,{{\it \_a}}^{4}+3\,{{\it \_a}}^{2}- \left ( 2\,{{\it \_a}}^{2}+1 \right ) ^{{\frac {3}{2}}}+1 \right ) \left ( 2\,{{\it \_a}}^{2}+1 \right ) ^{-{\frac {5}{2}}}}}}}}+2\,{{\it \_a}}^{2}\sqrt [3]{{\frac {{\it \_a}\, \left ( 2\,{{\it \_a}}^{4}+3\,{{\it \_a}}^{2}- \left ( 2\,{{\it \_a}}^{2}+1 \right ) ^{3/2}+1 \right ) }{ \left ( 2\,{{\it \_a}}^{2}+1 \right ) ^{5/2}}}}-{\it \_a}+\sqrt [3]{{{\it \_a} \left ( 2\,{{\it \_a}}^{4}+3\,{{\it \_a}}^{2}- \left ( 2\,{{\it \_a}}^{2}+1 \right ) ^{{\frac {3}{2}}}+1 \right ) \left ( 2\,{{\it \_a}}^{2}+1 \right ) ^{-{\frac {5}{2}}}}} \right ) }{d{\it \_a}}-{\it \_C1}=0,\ln \left ( x \right ) -\int ^{{\frac {y \left ( x \right ) }{x}}}\!{\frac {1}{4\,{{\it \_a}}^{2}+4} \left ( {{{\it \_a}}^{2} \left ( i\sqrt {3}+1 \right ) {\frac {1}{\sqrt [3]{{{\it \_a} \left ( 2\,{{\it \_a}}^{4}+3\,{{\it \_a}}^{2}- \left ( 2\,{{\it \_a}}^{2}+1 \right ) ^{{\frac {3}{2}}}+1 \right ) \left ( 2\,{{\it \_a}}^{2}+1 \right ) ^{-{\frac {5}{2}}}}}}}}+2\, \left ( \left ( i\sqrt {3}-1 \right ) \sqrt [3]{{\frac {{\it \_a}\, \left ( 2\,{{\it \_a}}^{4}+3\,{{\it \_a}}^{2}- \left ( 2\,{{\it \_a}}^{2}+1 \right ) ^{3/2}+1 \right ) }{ \left ( 2\,{{\it \_a}}^{2}+1 \right ) ^{5/2}}}}-2\,{\it \_a} \right ) \left ( {{\it \_a}}^{2}+1/2 \right ) \right ) \left ( {{\it \_a}}^{2}+{\frac {1}{2}} \right ) ^{-1}}{d{\it \_a}}-{\it \_C1}=0,\ln \left ( x \right ) -\int ^{{\frac {y \left ( x \right ) }{x}}}\!{\frac {1}{4\,{{\it \_a}}^{2}+4} \left ( -{ \left ( i\sqrt {3}-1 \right ) {{\it \_a}}^{2}{\frac {1}{\sqrt [3]{{{\it \_a} \left ( 2\,{{\it \_a}}^{4}+3\,{{\it \_a}}^{2}- \left ( 2\,{{\it \_a}}^{2}+1 \right ) ^{{\frac {3}{2}}}+1 \right ) \left ( 2\,{{\it \_a}}^{2}+1 \right ) ^{-{\frac {5}{2}}}}}}}}-2\, \left ( \left ( i\sqrt {3}+1 \right ) \sqrt [3]{{\frac {{\it \_a}\, \left ( 2\,{{\it \_a}}^{4}+3\,{{\it \_a}}^{2}- \left ( 2\,{{\it \_a}}^{2}+1 \right ) ^{3/2}+1 \right ) }{ \left ( 2\,{{\it \_a}}^{2}+1 \right ) ^{5/2}}}}+2\,{\it \_a} \right ) \left ( {{\it \_a}}^{2}+1/2 \right ) \right ) \left ( {{\it \_a}}^{2}+{\frac {1}{2}} \right ) ^{-1}}{d{\it \_a}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[x + 3*y[x]*y'[x] + 2*y[x]*y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(2*y(x)*diff(y(x),x)^3+3*y(x)*diff(y(x),x)+x = 0, y(x),'implicit')
Maple raw output
1/2*x^2+y(x)^2 = 0, ln(x)-Intat((-2*_a^3-_a^2/(_a*(2*_a^4+3*_a^2-(2*_a^2+1)^(3/2)+1)/(2*_a^2+1)^(5/2))^(1/3)+2*_a^2*(_a*(2*_a^4+3*_a^2-(2*_a^2+1)^(3/2)+1)/(2*_a^2+1)^(5/2))^(1/3)-_a+(_a*(2*_a^4+3*_a^2-(2*_a^2+1)^(3/2)+1)/(2*_a^2+1)^(5/2))^(1/3))/(2*_a^4+3*_a^2+1),_a = y(x)/x)-_C1 = 0, ln(x)-Intat(1/4*(-(I*3^(1/2)-1)*_a^2/(_a*(2*_a^4+3*_a^2-(2*_a^2+1)^(3/2)+1)/(2*_a^2+1)^(5/2))^(1/3)-2*((I*3^(1/2)+1)*(_a*(2*_a^4+3*_a^2-(2*_a^2+1)^(3/2)+1)/(2*_a^2+1)^(5/2))^(1/3)+2*_a)*(_a^2+1/2))/(_a^2+1/2)/(_a^2+1),_a = y(x)/x)-_C1 = 0, ln(x)-Intat(1/4*(_a^2*(I*3^(1/2)+1)/(_a*(2*_a^4+3*_a^2-(2*_a^2+1)^(3/2)+1)/(2*_a^2+1)^(5/2))^(1/3)+2*((I*3^(1/2)-1)*(_a*(2*_a^4+3*_a^2-(2*_a^2+1)^(3/2)+1)/(2*_a^2+1)^(5/2))^(1/3)-2*_a)*(_a^2+1/2))/(_a^2+1/2)/(_a^2+1),_a = y(x)/x)-_C1 = 0