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 = 0.00777399 (sec), leaf count = 51

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

Maple
cpu = 0.007 (sec), leaf count = 19

\[ \left \{ \left (y \relax (x ) \right ) ^{2}+{\frac {2}{5\,{x}^{3}}}-{{\it \_C1}{x}^{-{\frac {4}{3}}}}=0 \right \} \] 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),'implicit')

Maple raw output

y(x)^2+2/5/x^3-1/x^(4/3)*_C1 = 0