85.34.7 problem 7

Internal problem ID [22715]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. B Exercises at page 67
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:11:46 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&={\mathrm e}^{x +3 y}+1 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 23

ode:=diff(y(x),x) = exp(3*y(x)+x)+1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x}{3}+\frac {\ln \left (\frac {4}{{\mathrm e}^{-4 x} c_1 -3}\right )}{3} \]

✓ Mathematica. Time used: 0.662 (sec). Leaf size: 26

ode=D[y[x],x]==Exp[x+3*y[x]]+1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x-\frac {1}{3} \log \left (-\frac {3}{4} \left (e^{4 x}+4 c_1\right )\right ) \end{align*}

✓ Sympy. Time used: 2.000 (sec). Leaf size: 105

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(x + 3*y(x)) + Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \log {\left (2^{\frac {2}{3}} \sqrt [3]{\frac {e^{3 x}}{C_{1} - 3 e^{4 x}}} \right )}, \ y{\left (x \right )} = \log {\left (\frac {\sqrt [3]{\frac {e^{3 x}}{C_{1} - e^{4 x}}} \left (- 6^{\frac {2}{3}} - 3 \cdot 2^{\frac {2}{3}} \sqrt [6]{3} i\right )}{6} \right )}, \ y{\left (x \right )} = \log {\left (\frac {\sqrt [3]{\frac {e^{3 x}}{C_{1} - e^{4 x}}} \left (- 6^{\frac {2}{3}} + 3 \cdot 2^{\frac {2}{3}} \sqrt [6]{3} i\right )}{6} \right )}\right ] \]