8.2.10 problem 12

Internal problem ID [670]
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
Date solved : Monday, January 27, 2025 at 02:57:07 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=x \ln \left (y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

dsolve(diff(y(x),x) = x*ln(y(x)),y(x), singsol=all)
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (x^{2}+2 \,\operatorname {Ei}_{1}\left (-\textit {\_Z} \right )+2 c_1 \right )} \]

✓ Solution by Mathematica

Time used: 0.203 (sec). Leaf size: 22

DSolve[D[y[x],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*}