ODE
\[ a x^2 y'(x)=a x y(x)+b^2 y(x)^2+x^2 \] ODE Classification
[[_homogeneous, `class A`], _rational, _Riccati]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.0190003 (sec), leaf count = 23
\[\left \{\left \{y(x)\to \frac {x \tan \left (\frac {b \left (a c_1+\log (x)\right )}{a}\right )}{b}\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 24
\[ \left \{ {\frac {a}{b}\arctan \left ( {\frac {by \left ( x \right ) }{x}} \right ) }-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[a*x^2*y'[x] == x^2 + a*x*y[x] + b^2*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (x*Tan[(b*(a*C[1] + Log[x]))/a])/b}}
Maple raw input
dsolve(a*x^2*diff(y(x),x) = x^2+a*x*y(x)+b^2*y(x)^2, y(x),'implicit')
Maple raw output
a/b*arctan(b/x*y(x))-ln(x)-_C1 = 0