ODE
\[ (3-x) y''(x)-(9-4 x) y'(x)+3 (2-x) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.028233 (sec), leaf count = 42
\[\left \{\left \{y(x)\to \frac {1}{8} c_2 e^{3 x-9} \left (4 x^3-42 x^2+150 x-183\right )+c_1 e^{x-3}\right \}\right \}\]
Maple ✓
cpu = 0.039 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) ={{\rm e}^{x}}{\it \_C1}+{\it \_C2}\,{{\rm e}^{3\,x}} \left ( 4\,{x}^{3}-42\,{x}^{2}+150\,x-183 \right ) \right \} \] Mathematica raw input
DSolve[3*(2 - x)*y[x] - (9 - 4*x)*y'[x] + (3 - x)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^(-3 + x)*C[1] + (E^(-9 + 3*x)*(-183 + 150*x - 42*x^2 + 4*x^3)*C[2])/8}}
Maple raw input
dsolve((3-x)*diff(diff(y(x),x),x)-(9-4*x)*diff(y(x),x)+3*(2-x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = exp(x)*_C1+_C2*exp(3*x)*(4*x^3-42*x^2+150*x-183)