ODE
\[ x y'(x)=x^3+\left (1-2 x^2\right ) y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.164993 (sec), leaf count = 21
\[\left \{\left \{y(x)\to x \left (\frac {1}{2}+c_1 e^{-x^2}\right )\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 17
\[\left [y \left (x \right ) = \frac {x}{2}+x \,{\mathrm e}^{-x^{2}} \textit {\_C1}\right ]\] Mathematica raw input
DSolve[x*y'[x] == x^3 + (1 - 2*x^2)*y[x],y[x],x]
Mathematica raw output
{{y[x] -> x*(1/2 + C[1]/E^x^2)}}
Maple raw input
dsolve(x*diff(y(x),x) = x^3+(-2*x^2+1)*y(x), y(x))
Maple raw output
[y(x) = 1/2*x+x*exp(-x^2)*_C1]