4.7.21 \(x^2+(x-3) (x-2) y'(x)+3 x y(x)-8 y(x)=0\)

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 = 0.0123187 (sec), leaf count = 34

\[\left \{\left \{y(x)\to \frac {-12 c_1-3 x^4+8 x^3}{12 (x-3) (x-2)^2}\right \}\right \}\]

Maple
cpu = 0.018 (sec), leaf count = 27

\[ \left \{ y \relax (x ) ={\frac {1}{ \left (x-3 \right ) \left (x-2 \right ) ^{2}} \left (-{\frac {{x}^{4}}{4}}+{\frac {2\,{x}^{3}}{3}}+{\it \_C1} \right ) } \right \} \] 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),'implicit')

Maple raw output

y(x) = (-1/4*x^4+2/3*x^3+_C1)/(x-3)/(x-2)^2