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

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00881329 (sec), leaf count = 24

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

Maple
cpu = 0.009 (sec), leaf count = 21

\[ \left \{ y \relax (x ) =-{\frac {a{x}^{2}}{-2+b}}+{x}^{b}{\it \_C1} \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> (a*x^2)/(2 - b) + x^b*C[1]}}

Maple raw input

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

Maple raw output

y(x) = -1/(-2+b)*a*x^2+x^b*_C1