Internal problem ID [2762]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 1
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-x \left (x^{2}-y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(x),x) = x*(x^2-y(x)),y(x), singsol=all)
\[ y \relax (x ) = x^{2}-2+{\mathrm e}^{-\frac {x^{2}}{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 22
DSolve[y'[x]==x*(x^2-y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2+c_1 e^{-\frac {x^2}{2}}-2 \\ \end{align*}