4.6.29 \(x^2 y'(x)=3 x \tan (y(x))+\sec (y(x))\)

ODE
\[ x^2 y'(x)=3 x \tan (y(x))+\sec (y(x)) \] ODE Classification

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

Book solution method
Change of Variable, new dependent variable

Mathematica
cpu = 0.15135 (sec), leaf count = 23

\[\left \{\left \{y(x)\to -\sin ^{-1}\left (3 c_1 x^3+\frac {1}{4 x}\right )\right \}\right \}\]

Maple
cpu = 0.443 (sec), leaf count = 18

\[ \left \{ 4\,{\frac {\sin \left (y \relax (x ) \right ) }{{x}^{3}}}+{x}^{-4}-{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[x^2*y'[x] == Sec[y[x]] + 3*x*Tan[y[x]],y[x],x]

Mathematica raw output

{{y[x] -> -ArcSin[1/(4*x) + 3*x^3*C[1]]}}

Maple raw input

dsolve(x^2*diff(y(x),x) = sec(y(x))+3*x*tan(y(x)), y(x),'implicit')

Maple raw output

4/x^3*sin(y(x))+1/x^4-_C1 = 0