ODE
\[ x^2 y'(x)=a+b x+c x^2-x y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.16733 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {a \log (x)}{x}+b+\frac {c x}{2}+\frac {c_1}{x}\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 22
\[\left [y \left (x \right ) = \frac {c x}{2}+b +\frac {\ln \left (x \right ) a}{x}+\frac {\textit {\_C1}}{x}\right ]\] Mathematica raw input
DSolve[x^2*y'[x] == a + b*x + c*x^2 - x*y[x],y[x],x]
Mathematica raw output
{{y[x] -> b + (c*x)/2 + C[1]/x + (a*Log[x])/x}}
Maple raw input
dsolve(x^2*diff(y(x),x) = a+b*x+c*x^2-x*y(x), y(x))
Maple raw output
[y(x) = 1/2*c*x+b+1/x*ln(x)*a+1/x*_C1]