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

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00906 (sec), leaf count = 26

\[\left \{\left \{y(x)\to -\frac {a}{2 x}-b+c_1 x+c x \log (x)\right \}\right \}\]

Maple
cpu = 0.012 (sec), leaf count = 22

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

Maple raw output

y(x) = -b+x*c*ln(x)-1/2/x*a+_C1*x