ODE
\[ x y'(x)=a x^2+b y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.170336 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {a x^2}{2-b}+c_1 x^b\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 21
\[\left [y \left (x \right ) = -\frac {x^{2} a}{-2+b}+x^{b} \textit {\_C1}\right ]\] 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))
Maple raw output
[y(x) = -1/(-2+b)*x^2*a+x^b*_C1]