4.4.13 \(x y'(x)=x^3+\left (1-2 x^2\right ) y(x)\)

ODE
\[ x y'(x)=x^3+\left (1-2 x^2\right ) y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00817173 (sec), leaf count = 21

\[\left \{\left \{y(x)\to x \left (c_1 e^{-x^2}+\frac {1}{2}\right )\right \}\right \}\]

Maple
cpu = 0.008 (sec), leaf count = 17

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

Maple raw output

y(x) = 1/2*x+exp(-x^2)*x*_C1