4.1.8 \(y'(x)=x \left (x^2-y(x)\right )\)

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00635294 (sec), leaf count = 22

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

Maple
cpu = 0.031 (sec), leaf count = 17

\[ \left \{ y \relax (x ) ={x}^{2}-2+{{\rm e}^{-{\frac {{x}^{2}}{2}}}}{\it \_C1} \right \} \] Mathematica raw input

DSolve[y'[x] == x*(x^2 - y[x]),y[x],x]

Mathematica raw output

{{y[x] -> -2 + x^2 + C[1]/E^(x^2/2)}}

Maple raw input

dsolve(diff(y(x),x) = x*(x^2-y(x)), y(x),'implicit')

Maple raw output

y(x) = x^2-2+exp(-1/2*x^2)*_C1