89.7.12 problem 12

Internal problem ID [24443]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 61
Problem number : 12
Date solved : Thursday, October 02, 2025 at 10:35:08 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y^{\prime }&=1+6 x \,{\mathrm e}^{x -y} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 15

ode:=diff(y(x),x) = 1+6*x*exp(x-y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \ln \left ({\mathrm e}^{x} \left (3 x^{2}+c_1 \right )\right ) \]

✓ Mathematica. Time used: 0.246 (sec). Leaf size: 16

ode=D[y[x],x]==1+6*x*Exp[x- y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x+\log \left (3 x^2+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.372 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x*exp(x - y(x)) + Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \log {\left (\left (C_{1} + 3 x^{2}\right ) e^{x} \right )} \]