4.5.33 \((a+x) y'(x)+b x^2+y(x)=0\)

ODE
\[ (a+x) y'(x)+b x^2+y(x)=0 \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00539683 (sec), leaf count = 25

\[\left \{\left \{y(x)\to \frac {3 c_1-b x^3}{3 (a+x)}\right \}\right \}\]

Maple
cpu = 0.005 (sec), leaf count = 24

\[ \left \{ y \relax (x ) ={\frac {-b{x}^{3}+3\,{\it \_C1}}{3\,a+3\,x}} \right \} \] Mathematica raw input

DSolve[b*x^2 + y[x] + (a + x)*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (-(b*x^3) + 3*C[1])/(3*(a + x))}}

Maple raw input

dsolve((a+x)*diff(y(x),x)+b*x^2+y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (-b*x^3+3*_C1)/(3*a+3*x)