ODE
\[ (1-3 x)^2 y''(x)-3 (1-3 x) y'(x)-9 y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.174577 (sec), leaf count = 39
\[\left \{\left \{y(x)\to \frac {c_1 \left (-9 x^2+6 x-2\right )-3 i c_2 x (3 x-2)}{6 x-2}\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 17
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x -\frac {1}{3}}+\textit {\_C2} \left (x -\frac {1}{3}\right )\right ]\] Mathematica raw input
DSolve[-9*y[x] - 3*(1 - 3*x)*y'[x] + (1 - 3*x)^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((-2 + 6*x - 9*x^2)*C[1] - (3*I)*x*(-2 + 3*x)*C[2])/(-2 + 6*x)}}
Maple raw input
dsolve((1-3*x)^2*diff(diff(y(x),x),x)-3*(1-3*x)*diff(y(x),x)-9*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1/(x-1/3)+_C2*(x-1/3)]