76.2.2 problem 2

Internal problem ID [17338]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 10:01:40 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

dsolve(diff(y(t),t)-2*y(t)=t^2*exp(2*t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 22

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

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