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]
Solve \begin {gather*} \boxed {y^{\prime }-x \ln \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.041 (sec). Leaf size: 20
dsolve(diff(y(x),x) = x*ln(y(x)),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (x^{2}+2 \expIntegral \left (1, -\textit {\_Z} \right )+2 c_{1}\right )} \]
✓ Solution by Mathematica
Time used: 0.245 (sec). Leaf size: 22
DSolve[y'[x] == x*Log[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \operatorname {LogIntegral}^{(-1)}\left (\frac {x^2}{2}+c_1\right ) \\ y(x)\to 1 \\ \end{align*}