78.1.39 problem 4 (a)

Internal problem ID [18094]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 4 (a)
Date solved : Tuesday, January 28, 2025 at 11:26:04 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&={\mathrm e}^{3 x -2 y} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.077 (sec). Leaf size: 20

dsolve([diff(y(x),x)=exp(3*x-2*y(x)),y(0) = 0],y(x), singsol=all)
 

\[ y = -\frac {\ln \left (3\right )}{2}+\frac {\ln \left (1+2 \,{\mathrm e}^{3 x}\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.828 (sec). Leaf size: 23

DSolve[{D[y[x],x]==Exp[3*x-2*y[x]],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

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