ODE
\[ \left (x^2+1\right ) y'(x)=x \left (3 x^2-y(x)\right ) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.0114468 (sec), leaf count = 22
\[\left \{\left \{y(x)\to \frac {c_1}{\sqrt {x^2+1}}+x^2-2\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) ={x}^{2}-2+{{\it \_C1}{\frac {1}{\sqrt {{x}^{2}+1}}}} \right \} \] Mathematica raw input
DSolve[(1 + x^2)*y'[x] == x*(3*x^2 - y[x]),y[x],x]
Mathematica raw output
{{y[x] -> -2 + x^2 + C[1]/Sqrt[1 + x^2]}}
Maple raw input
dsolve((x^2+1)*diff(y(x),x) = x*(3*x^2-y(x)), y(x),'implicit')
Maple raw output
y(x) = x^2-2+1/(x^2+1)^(1/2)*_C1