4.7.46 \(x^3 y'(x)=a+b x^2 y(x)\)

ODE
\[ x^3 y'(x)=a+b x^2 y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00990763 (sec), leaf count = 23

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

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

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

Maple raw output

y(x) = -1/(2+b)*a/x^2+x^b*_C1