ODE
\[ 2 y(x) y'(x)^3-3 x y'(x)+2 y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _dAlembert]
Book solution method
No Missing Variables ODE, Solve for \(x\)
Mathematica ✗
cpu = 599.999 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.056 (sec), leaf count = 517
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{3}-{\frac {{x}^{3}}{2}}=0,\ln \left ( x \right ) -\int ^{{\frac {y \left ( x \right ) }{x}}}\!{\frac {1}{4\,{{\it \_a}}^{4}-2\,{\it \_a}} \left ( -2\,{\frac { \left ( i\sqrt {3}-1 \right ) \left ( {{\it \_a}}^{3}-1/2 \right ) }{\sqrt [3]{ \left ( \sqrt {2}\sqrt { \left ( 2\,{{\it \_a}}^{4}-{\it \_a} \right ) ^{-1}}{{\it \_a}}^{2}+1 \right ) \left ( 2\,{{\it \_a}}^{3}-1 \right ) ^{2}}}}-i\sqrt {3}\sqrt [3]{ \left ( \sqrt {2}\sqrt { \left ( 2\,{{\it \_a}}^{4}-{\it \_a} \right ) ^{-1}}{{\it \_a}}^{2}+1 \right ) \left ( 2\,{{\it \_a}}^{3}-1 \right ) ^{2}}-4\,{{\it \_a}}^{3}-\sqrt [3]{ \left ( \sqrt {2}\sqrt { \left ( 2\,{{\it \_a}}^{4}-{\it \_a} \right ) ^{-1}}{{\it \_a}}^{2}+1 \right ) \left ( 2\,{{\it \_a}}^{3}-1 \right ) ^{2}}+2 \right ) }{d{\it \_a}}-{\it \_C1}=0,\ln \left ( x \right ) -\int ^{{\frac {y \left ( x \right ) }{x}}}\!{\frac {1}{4\,{{\it \_a}}^{4}-2\,{\it \_a}} \left ( 2\,{\frac { \left ( i\sqrt {3}+1 \right ) \left ( {{\it \_a}}^{3}-1/2 \right ) }{\sqrt [3]{ \left ( \sqrt {2}\sqrt { \left ( 2\,{{\it \_a}}^{4}-{\it \_a} \right ) ^{-1}}{{\it \_a}}^{2}+1 \right ) \left ( 2\,{{\it \_a}}^{3}-1 \right ) ^{2}}}}+i\sqrt {3}\sqrt [3]{ \left ( \sqrt {2}\sqrt { \left ( 2\,{{\it \_a}}^{4}-{\it \_a} \right ) ^{-1}}{{\it \_a}}^{2}+1 \right ) \left ( 2\,{{\it \_a}}^{3}-1 \right ) ^{2}}-4\,{{\it \_a}}^{3}-\sqrt [3]{ \left ( \sqrt {2}\sqrt { \left ( 2\,{{\it \_a}}^{4}-{\it \_a} \right ) ^{-1}}{{\it \_a}}^{2}+1 \right ) \left ( 2\,{{\it \_a}}^{3}-1 \right ) ^{2}}+2 \right ) }{d{\it \_a}}-{\it \_C1}=0,\ln \left ( x \right ) -\int ^{{\frac {y \left ( x \right ) }{x}}}\!{\frac {1}{{\it \_a}\, \left ( 2\,{{\it \_a}}^{3}-1 \right ) } \left ( \left ( -2\,\sqrt [3]{ \left ( \sqrt {2}\sqrt { \left ( 2\,{{\it \_a}}^{4}-{\it \_a} \right ) ^{-1}}{{\it \_a}}^{2}+1 \right ) \left ( 2\,{{\it \_a}}^{3}-1 \right ) ^{2}}-2 \right ) {{\it \_a}}^{3}+ \left ( \left ( \sqrt {2}\sqrt { \left ( 2\,{{\it \_a}}^{4}-{\it \_a} \right ) ^{-1}}{{\it \_a}}^{2}+1 \right ) \left ( 2\,{{\it \_a}}^{3}-1 \right ) ^{2} \right ) ^{{\frac {2}{3}}}+\sqrt [3]{ \left ( \sqrt {2}\sqrt { \left ( 2\,{{\it \_a}}^{4}-{\it \_a} \right ) ^{-1}}{{\it \_a}}^{2}+1 \right ) \left ( 2\,{{\it \_a}}^{3}-1 \right ) ^{2}}+1 \right ) {\frac {1}{\sqrt [3]{ \left ( \sqrt {2}\sqrt { \left ( 2\,{{\it \_a}}^{4}-{\it \_a} \right ) ^{-1}}{{\it \_a}}^{2}+1 \right ) \left ( 2\,{{\it \_a}}^{3}-1 \right ) ^{2}}}}}{d{\it \_a}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[2*y[x] - 3*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*x*diff(y(x),x)+2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x)^3-1/2*x^3 = 0, ln(x)-Intat(((-2*((2^(1/2)*(1/(2*_a^4-_a))^(1/2)*_a^2+1)*(2*_a^3-1)^2)^(1/3)-2)*_a^3+((2^(1/2)*(1/(2*_a^4-_a))^(1/2)*_a^2+1)*(2*_a^3-1)^2)^(2/3)+((2^(1/2)*(1/(2*_a^4-_a))^(1/2)*_a^2+1)*(2*_a^3-1)^2)^(1/3)+1)/_a/(2*_a^3-1)/((2^(1/2)*(1/(2*_a^4-_a))^(1/2)*_a^2+1)*(2*_a^3-1)^2)^(1/3),_a = y(x)/x)-_C1 = 0, ln(x)-Intat((-2*(I*3^(1/2)-1)*(_a^3-1/2)/((2^(1/2)*(1/(2*_a^4-_a))^(1/2)*_a^2+1)*(2*_a^3-1)^2)^(1/3)-I*3^(1/2)*((2^(1/2)*(1/(2*_a^4-_a))^(1/2)*_a^2+1)*(2*_a^3-1)^2)^(1/3)-4*_a^3-((2^(1/2)*(1/(2*_a^4-_a))^(1/2)*_a^2+1)*(2*_a^3-1)^2)^(1/3)+2)/(4*_a^4-2*_a),_a = y(x)/x)-_C1 = 0, ln(x)-Intat((2*(I*3^(1/2)+1)*(_a^3-1/2)/((2^(1/2)*(1/(2*_a^4-_a))^(1/2)*_a^2+1)*(2*_a^3-1)^2)^(1/3)+I*3^(1/2)*((2^(1/2)*(1/(2*_a^4-_a))^(1/2)*_a^2+1)*(2*_a^3-1)^2)^(1/3)-4*_a^3-((2^(1/2)*(1/(2*_a^4-_a))^(1/2)*_a^2+1)*(2*_a^3-1)^2)^(1/3)+2)/(4*_a^4-2*_a),_a = y(x)/x)-_C1 = 0