ODE
\[ x^2+(x-3) (x-2) y'(x)+3 x y(x)-8 y(x)=0 \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.176162 (sec), leaf count = 34
\[\left \{\left \{y(x)\to \frac {-3 x^4+8 x^3-12 c_1}{12 (x-3) (x-2)^2}\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 27
\[\left [y \left (x \right ) = \frac {-\frac {1}{4} x^{4}+\frac {2}{3} x^{3}+\textit {\_C1}}{\left (x -3\right ) \left (x -2\right )^{2}}\right ]\] Mathematica raw input
DSolve[x^2 - 8*y[x] + 3*x*y[x] + (-3 + x)*(-2 + x)*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (8*x^3 - 3*x^4 - 12*C[1])/(12*(-3 + x)*(-2 + x)^2)}}
Maple raw input
dsolve((x-2)*(x-3)*diff(y(x),x)+x^2-8*y(x)+3*x*y(x) = 0, y(x))
Maple raw output
[y(x) = (-1/4*x^4+2/3*x^3+_C1)/(x-3)/(x-2)^2]