##### 4.12.42 $$3 x^4 y(x) y'(x)=1-2 x^3 y(x)^2$$

ODE
$3 x^4 y(x) y'(x)=1-2 x^3 y(x)^2$ ODE Classiﬁcation

[[_homogeneous, class G], _rational, _Bernoulli]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.314666 (sec), leaf count = 51

$\left \{\left \{y(x)\to -\sqrt {-\frac {2}{5 x^3}+\frac {c_1}{x^{4/3}}}\right \},\left \{y(x)\to \sqrt {-\frac {2}{5 x^3}+\frac {c_1}{x^{4/3}}}\right \}\right \}$

Maple
cpu = 0.036 (sec), leaf count = 55

$\left [y \left (x \right ) = -\frac {\sqrt {-5 x^{\frac {13}{3}} \left (2 x^{\frac {4}{3}}-5 \textit {\_C1} \,x^{3}\right )}}{5 x^{\frac {13}{3}}}, y \left (x \right ) = \frac {\sqrt {-5 x^{\frac {13}{3}} \left (2 x^{\frac {4}{3}}-5 \textit {\_C1} \,x^{3}\right )}}{5 x^{\frac {13}{3}}}\right ]$ Mathematica raw input

DSolve[3*x^4*y[x]*y'[x] == 1 - 2*x^3*y[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> -Sqrt[-2/(5*x^3) + C[1]/x^(4/3)]}, {y[x] -> Sqrt[-2/(5*x^3) + C[1]/x^(
4/3)]}}

Maple raw input

dsolve(3*x^4*y(x)*diff(y(x),x) = 1-2*x^3*y(x)^2, y(x))

Maple raw output

[y(x) = -1/5/x^(13/3)*(-5*x^(13/3)*(2*x^(4/3)-5*_C1*x^3))^(1/2), y(x) = 1/5/x^(1
3/3)*(-5*x^(13/3)*(2*x^(4/3)-5*_C1*x^3))^(1/2)]