##### 4.14.15 $$x^3+x^2 y(x)^2 y'(x)-x+1=0$$

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 = 0.268672 (sec), leaf count = 111

$\left \{\left \{y(x)\to -\frac {\sqrt [3]{-\frac {3}{2}} \sqrt [3]{-x^3+2 x \log (x)+2 c_1 x+2}}{\sqrt [3]{x}}\right \},\left \{y(x)\to \frac {\sqrt [3]{-\frac {3 x^3}{2}+3 x \log (x)+3 c_1 x+3}}{\sqrt [3]{x}}\right \},\left \{y(x)\to \frac {(-1)^{2/3} \sqrt [3]{-\frac {3 x^3}{2}+3 x \log (x)+3 c_1 x+3}}{\sqrt [3]{x}}\right \}\right \}$

Maple
cpu = 0.04 (sec), leaf count = 155

$\left [y \left (x \right ) = \frac {\left (\left (-12 x^{3}+24 x \ln \left (x \right )+8 x \textit {\_C1} +24\right ) x^{2}\right )^{\frac {1}{3}}}{2 x}, y \left (x \right ) = -\frac {\left (\left (-12 x^{3}+24 x \ln \left (x \right )+8 x \textit {\_C1} +24\right ) x^{2}\right )^{\frac {1}{3}}}{4 x}-\frac {i \sqrt {3}\, \left (\left (-12 x^{3}+24 x \ln \left (x \right )+8 x \textit {\_C1} +24\right ) x^{2}\right )^{\frac {1}{3}}}{4 x}, y \left (x \right ) = -\frac {\left (\left (-12 x^{3}+24 x \ln \left (x \right )+8 x \textit {\_C1} +24\right ) x^{2}\right )^{\frac {1}{3}}}{4 x}+\frac {i \sqrt {3}\, \left (\left (-12 x^{3}+24 x \ln \left (x \right )+8 x \textit {\_C1} +24\right ) x^{2}\right )^{\frac {1}{3}}}{4 x}\right ]$ 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))

Maple raw output

[y(x) = 1/2/x*((-12*x^3+24*x*ln(x)+8*x*_C1+24)*x^2)^(1/3), y(x) = -1/4/x*((-12*x
^3+24*x*ln(x)+8*x*_C1+24)*x^2)^(1/3)-1/4*I*3^(1/2)/x*((-12*x^3+24*x*ln(x)+8*x*_C
1+24)*x^2)^(1/3), y(x) = -1/4/x*((-12*x^3+24*x*ln(x)+8*x*_C1+24)*x^2)^(1/3)+1/4*
I*3^(1/2)/x*((-12*x^3+24*x*ln(x)+8*x*_C1+24)*x^2)^(1/3)]