4.6.4 \(x^2 y'(x)=a+b x+c x^2-x y(x)\)

ODE
\[ x^2 y'(x)=a+b x+c x^2-x y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00691771 (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

\[ \left \{ y \relax (x ) ={\frac {cx}{2}}+b+{\frac {a\ln \relax (x ) }{x}}+{\frac {{\it \_C1}}{x}} \right \} \] 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),'implicit')

Maple raw output

y(x) = 1/2*c*x+b+1/x*ln(x)*a+1/x*_C1