73.3.16 problem 4.4 (f)

Internal problem ID [15050]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.4 (f)
Date solved : Tuesday, January 28, 2025 at 07:28:41 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.871 (sec). Leaf size: 24

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

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