ODE
\[ (2-x)^2 y''(x)+(2-x) y'(x)-3 y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.170512 (sec), leaf count = 22
\[\left \{\left \{y(x)\to c_1 (x-2)^3+\frac {c_2}{x-2}\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 19
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x -2}+\textit {\_C2} \left (x -2\right )^{3}\right ]\] Mathematica raw input
DSolve[-3*y[x] + (2 - x)*y'[x] + (2 - x)^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-2 + x)^3*C[1] + C[2]/(-2 + x)}}
Maple raw input
dsolve((2-x)^2*diff(diff(y(x),x),x)+(2-x)*diff(y(x),x)-3*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1/(x-2)+_C2*(x-2)^3]