73.7.45 problem 45

Internal problem ID [15132]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 45
Date solved : Monday, March 31, 2025 at 01:26:39 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&={\mathrm e}^{4 x +3 y} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 26

ode:=diff(y(x),x) = exp(4*x+3*y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\ln \left (3\right )}{3}+\frac {2 \ln \left (2\right )}{3}-\frac {\ln \left (-{\mathrm e}^{4 x}-4 c_1 \right )}{3} \]

✓ Mathematica. Time used: 0.88 (sec). Leaf size: 24

ode=D[y[x],x]==Exp[4*x+3*y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {1}{3} \log \left (-\frac {3}{4} \left (e^{4 x}+4 c_1\right )\right ) \]

✓ Sympy. Time used: 1.917 (sec). Leaf size: 100

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(4*x + 3*y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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