ODE
\[ x^3 y'(x)=a+b x^2 y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.171374 (sec), leaf count = 23
\[\left \{\left \{y(x)\to -\frac {a}{(b+2) x^2}+c_1 x^b\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 21
\[\left [y \left (x \right ) = -\frac {a}{\left (2+b \right ) x^{2}}+x^{b} \textit {\_C1}\right ]\] Mathematica raw input
DSolve[x^3*y'[x] == a + b*x^2*y[x],y[x],x]
Mathematica raw output
{{y[x] -> -(a/((2 + b)*x^2)) + x^b*C[1]}}
Maple raw input
dsolve(x^3*diff(y(x),x) = a+b*x^2*y(x), y(x))
Maple raw output
[y(x) = -1/(2+b)/x^2*a+x^b*_C1]