ODE
\[ (1-x) x y''(x)-3 y'(x)+2 y(x)=x \left (3 x^3+1\right ) \] ODE Classification
[[_2nd_order, _exact, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.034747 (sec), leaf count = 51
\[\left \{\left \{y(x)\to \frac {60 c_1 x^4+20 c_2 x-15 c_2-18 x^6+36 x^5+30 x^3-15 x^2}{60 (x-1)^2}\right \}\right \}\]
Maple ✓
cpu = 0.032 (sec), leaf count = 45
\[ \left \{ y \left ( x \right ) ={\frac {-6\,{x}^{6}+20\,{\it \_C2}\,{x}^{4}+12\,{x}^{5}+10\,{x}^{3}+80\,{\it \_C1}\,x-5\,{x}^{2}-60\,{\it \_C1}}{20\, \left ( -1+x \right ) ^{2}}} \right \} \] Mathematica raw input
DSolve[2*y[x] - 3*y'[x] + (1 - x)*x*y''[x] == x*(1 + 3*x^3),y[x],x]
Mathematica raw output
{{y[x] -> (-15*x^2 + 30*x^3 + 36*x^5 - 18*x^6 + 60*x^4*C[1] - 15*C[2] + 20*x*C[2])/(60*(-1 + x)^2)}}
Maple raw input
dsolve(x*(1-x)*diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = x*(3*x^3+1), y(x),'implicit')
Maple raw output
y(x) = 1/20*(-6*x^6+20*_C2*x^4+12*x^5+10*x^3+80*_C1*x-5*x^2-60*_C1)/(-1+x)^2