15.19.12 problem 12

Internal problem ID [3296]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 37, page 171
Problem number : 12
Date solved : Sunday, March 30, 2025 at 01:33:01 AM
CAS classification : [_separable]

\begin{align*} y&=x +3 \ln \left (y^{\prime }\right ) \end{align*}

✓ Maple. Time used: 0.107 (sec). Leaf size: 25

ode:=y(x) = x+3*ln(diff(y(x),x)); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= x \\ y &= x +3 \ln \left (\frac {c_1}{-{\mathrm e}^{\frac {x}{3}}+c_1}\right ) \\ \end{align*}

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 22

ode=y[x]==x+3*Log[D[y[x],x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -3 \log \left (e^{-x/3}-\frac {c_1}{3}\right ) \]

✓ Sympy. Time used: 0.353 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + y(x) - 3*log(Derivative(y(x), x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 3 \log {\left (- \frac {e^{\frac {x}{3}}}{C_{1} e^{\frac {x}{3}} - 3} \right )} + 3 \log {\left (3 \right )} \]