4.8.5 \(x^3 y'(x)=\cos (y(x)) \left (\cos (y(x))-2 x^2 \sin (y(x))\right )\)

ODE
\[ x^3 y'(x)=\cos (y(x)) \left (\cos (y(x))-2 x^2 \sin (y(x))\right ) \] ODE Classification

[`y=_G(x,y')`]

Book solution method
Change of Variable, new dependent variable

Mathematica
cpu = 0.1503 (sec), leaf count = 17

\[\left \{\left \{y(x)\to \tan ^{-1}\left (\frac {4 c_1+\log (x)}{x^2}\right )\right \}\right \}\]

Maple
cpu = 0.45 (sec), leaf count = 17

\[ \left \{ -{x}^{2}\tan \left (y \relax (x ) \right ) +\ln \relax (x ) -{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[x^3*y'[x] == Cos[y[x]]*(Cos[y[x]] - 2*x^2*Sin[y[x]]),y[x],x]

Mathematica raw output

{{y[x] -> ArcTan[(4*C[1] + Log[x])/x^2]}}

Maple raw input

dsolve(x^3*diff(y(x),x) = cos(y(x))*(cos(y(x))-2*x^2*sin(y(x))), y(x),'implicit')

Maple raw output

-x^2*tan(y(x))+ln(x)-_C1 = 0