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 = 0.364027 (sec), leaf count = 23
\[\left \{\left \{y(x)\to -\sin ^{-1}\left (\frac {1}{4 x}+3 c_1 x^3\right )\right \}\right \}\]
Maple ✓
cpu = 0.505 (sec), leaf count = 17
\[\left [y \left (x \right ) = \arcsin \left (\frac {\textit {\_C1} \,x^{4}-1}{4 x}\right )\right ]\] 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))
Maple raw output
[y(x) = arcsin(1/4*(_C1*x^4-1)/x)]