10.1.2 problem 2

Internal problem ID [1099]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 2
Date solved : Monday, January 27, 2025 at 04:33:23 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 22

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

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