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 = 0.17565 (sec), leaf count = 51
\[\left \{\left \{y(x)\to \frac {-18 x^6+36 x^5+60 c_1 x^4+30 x^3-15 x^2+20 c_2 x-15 c_2}{60 (x-1)^2}\right \}\right \}\]
Maple ✓
cpu = 0.118 (sec), leaf count = 52
\[\left [y \left (x \right ) = \frac {\left (4 x -3\right ) \textit {\_C1}}{\left (x -1\right )^{2}}+\frac {x^{4} \textit {\_C2}}{\left (x -1\right )^{2}}-\frac {\left (6 x^{4}-12 x^{3}-10 x +5\right ) x^{2}}{20 \left (x -1\right )^{2}}\right ]\] 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))
Maple raw output
[y(x) = (4*x-3)/(x-1)^2*_C1+x^4/(x-1)^2*_C2-1/20*(6*x^4-12*x^3-10*x+5)*x^2/(x-1)^2]