74.4.17 problem 17

Internal problem ID [15910]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 08:19:07 AM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.947 (sec). Leaf size: 24

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

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