ODE
\[ (1-x) x^2 y''(x)-(4-5 x) x y'(x)+(6-9 x) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0274215 (sec), leaf count = 24
\[\left \{\left \{y(x)\to x^2 \left (c_1 x-c_2 (x \log (x)+1)\right )\right \}\right \}\]
Maple ✓
cpu = 0.025 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) ={x}^{2} \left ( \ln \left ( x \right ) {\it \_C2}\,x+{\it \_C1}\,x+{\it \_C2} \right ) \right \} \] Mathematica raw input
DSolve[(6 - 9*x)*y[x] - (4 - 5*x)*x*y'[x] + (1 - x)*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x^2*(x*C[1] - C[2]*(1 + x*Log[x]))}}
Maple raw input
dsolve(x^2*(1-x)*diff(diff(y(x),x),x)-x*(4-5*x)*diff(y(x),x)+(6-9*x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x^2*(ln(x)*_C2*x+_C1*x+_C2)