44.5.7 problem 7

Internal problem ID [7069]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 7
Date solved : Monday, January 27, 2025 at 02:46:46 PM
CAS classification : [_separable]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x)=exp(3*x+2*y(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.861 (sec). Leaf size: 24

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

\[ y(x)\to -\frac {1}{2} \log \left (-\frac {2}{3} \left (e^{3 x}+3 c_1\right )\right ) \]