ODE
\[ x^3 y''(x)-x^2 y'(x)=3-x^2 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0139757 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \frac {c_1 x^2}{2}+c_2+x+\frac {1}{x}\right \}\right \}\]
Maple ✓
cpu = 0.022 (sec), leaf count = 16
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,{x}^{2}}{2}}+{x}^{-1}+x+{\it \_C2} \right \} \] Mathematica raw input
DSolve[-(x^2*y'[x]) + x^3*y''[x] == 3 - x^2,y[x],x]
Mathematica raw output
{{y[x] -> x^(-1) + x + (x^2*C[1])/2 + C[2]}}
Maple raw input
dsolve(x^3*diff(diff(y(x),x),x)-x^2*diff(y(x),x) = -x^2+3, y(x),'implicit')
Maple raw output
y(x) = 1/2*_C1*x^2+1/x+x+_C2