Internal problem ID [20]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.3. Slope fields and solution curves. Page 26
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-x \ln \left (y\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x) = x*ln(y(x)),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (x^{2}+2 \,\operatorname {Ei}_{1}\left (-\textit {\_Z} \right )+2 c_{1} \right )} \]
✓ Solution by Mathematica
Time used: 0.266 (sec). Leaf size: 22
DSolve[y'[x] == x*Log[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {LogIntegral}^{(-1)}\left (\frac {x^2}{2}+c_1\right ) y(x)\to 1 \end{align*}