ODE
\[ x (a+b x) y''(x)+2 a y'(x)-2 b y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0346897 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \frac {\frac {c_2 (a+b x)^3}{b}+3 c_1}{3 x}\right \}\right \}\]
Maple ✓
cpu = 0.022 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}+{\it \_C2}\, \left ( bx+a \right ) ^{3}}{x}} \right \} \] Mathematica raw input
DSolve[-2*b*y[x] + 2*a*y'[x] + x*(a + b*x)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (3*C[1] + ((a + b*x)^3*C[2])/b)/(3*x)}}
Maple raw input
dsolve(x*(b*x+a)*diff(diff(y(x),x),x)+2*a*diff(y(x),x)-2*b*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C1+_C2*(b*x+a)^3)/x