ODE
\[ x^3+x^2 y(x)^2 y'(x)-x+1=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.00993195 (sec), leaf count = 111
\[\left \{\left \{y(x)\to -\frac {\sqrt [3]{-\frac {3}{2}} \sqrt [3]{2 c_1 x-x^3+2 x \log (x)+2}}{\sqrt [3]{x}}\right \},\left \{y(x)\to \frac {\sqrt [3]{3 c_1 x-\frac {3 x^3}{2}+3 x \log (x)+3}}{\sqrt [3]{x}}\right \},\left \{y(x)\to \frac {(-1)^{2/3} \sqrt [3]{3 c_1 x-\frac {3 x^3}{2}+3 x \log (x)+3}}{\sqrt [3]{x}}\right \}\right \}\]
Maple ✓
cpu = 0.006 (sec), leaf count = 25
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{3}+{\frac {3\,{x}^{2}}{2}}-3\,\ln \left ( x \right ) -3\,{x}^{-1}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[1 - x + x^3 + x^2*y[x]^2*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(((-3/2)^(1/3)*(2 - x^3 + 2*x*C[1] + 2*x*Log[x])^(1/3))/x^(1/3))}, {y[x] -> (3 - (3*x^3)/2 + 3*x*C[1] + 3*x*Log[x])^(1/3)/x^(1/3)}, {y[x] -> ((-1)^(2/3)*(3 - (3*x^3)/2 + 3*x*C[1] + 3*x*Log[x])^(1/3))/x^(1/3)}}
Maple raw input
dsolve(x^2*y(x)^2*diff(y(x),x)+1-x+x^3 = 0, y(x),'implicit')
Maple raw output
y(x)^3+3/2*x^2-3*ln(x)-3/x-_C1 = 0