ODE
\[ x y(x) y'(x)=a x^3 \cos (x)+y(x)^2 \] ODE Classification
[[_homogeneous, `class D`], _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.0227668 (sec), leaf count = 38
\[\left \{\left \{y(x)\to -x \sqrt {2 a \sin (x)+c_1}\right \},\left \{y(x)\to x \sqrt {2 a \sin (x)+c_1}\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 22
\[ \left \{ -2\,\sin \left ( x \right ) {x}^{2}a-{x}^{2}{\it \_C1}+ \left ( y \left ( x \right ) \right ) ^{2}=0 \right \} \] Mathematica raw input
DSolve[x*y[x]*y'[x] == a*x^3*Cos[x] + y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -(x*Sqrt[C[1] + 2*a*Sin[x]])}, {y[x] -> x*Sqrt[C[1] + 2*a*Sin[x]]}}
Maple raw input
dsolve(x*y(x)*diff(y(x),x) = a*x^3*cos(x)+y(x)^2, y(x),'implicit')
Maple raw output
-2*sin(x)*x^2*a-x^2*_C1+y(x)^2 = 0