74.5.35 problem 35

Internal problem ID [15999]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 35
Date solved : Tuesday, January 28, 2025 at 08:26:08 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 10

dsolve([diff(y(t),t)=exp(2*t)+2*y(t),y(0) = 0],y(t), singsol=all)
 

\[ y = t \,{\mathrm e}^{2 t} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 12

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

\[ y(t)\to e^{2 t} t \]