74.4.16 problem 16

Internal problem ID [15909]
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 : 16
Date solved : Tuesday, January 28, 2025 at 08:19:04 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&={\mathrm e}^{2 y+10 t} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 22

dsolve(diff(y(t),t)=exp(2*y(t)+10*t),y(t), singsol=all)
 

\[ y = \frac {\ln \left (5\right )}{2}-\frac {\ln \left (-{\mathrm e}^{10 t}-10 c_{1} \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.957 (sec). Leaf size: 24

DSolve[D[y[t],t]==Exp[2*y[t]+10*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {1}{2} \log \left (-\frac {e^{10 t}}{5}-2 c_1\right ) \]