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 = 0.0263269 (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 = 0.01 (sec), leaf count = 24
\[ \left \{ y \left ( x \right ) ={\frac {1}{9\,x-3} \left ( 9\, \left ( x-1/3 \right ) ^{2}{\it \_C2}+9\,{\it \_C1} \right ) } \right \} \] 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),'implicit')
Maple raw output
y(x) = (9*(x-1/3)^2*_C2+9*_C1)/(9*x-3)