2.2.10 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 : Tuesday, September 30, 2025 at 04:05:17 AM
CAS classification : [_separable]

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

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

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

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

✓ Mathematica. Time used: 0.133 (sec). Leaf size: 22

ode=D[y[x],x] == x*Log[y[x]]; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.162 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*log(y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \operatorname {li}{\left (y{\left (x \right )} \right )} = C_{1} + \frac {x^{2}}{2} \]