ODE
\[ x^2 y'(x)=a+b x+c x^2+x y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.167297 (sec), leaf count = 26
\[\left \{\left \{y(x)\to -\frac {a}{2 x}-b+c x \log (x)+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 22
\[\left [y \left (x \right ) = -b +x c \ln \left (x \right )-\frac {a}{2 x}+x \textit {\_C1}\right ]\] 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 - a/(2*x) + x*C[1] + c*x*Log[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) = -b+x*c*ln(x)-1/2*a/x+x*_C1]