14.11.14 problem 14

Internal problem ID [2607]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.5. Method of judicious guessing. Excercises page 164
Problem number : 14
Date solved : Monday, January 27, 2025 at 06:04:22 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }&=1+t^{2}+{\mathrm e}^{-2 t} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 33

dsolve(diff(y(t),t$2)+2*diff(y(t),t)=1+t^2+exp(-2*t),y(t), singsol=all)
 

\[ y = \frac {\left (-1-2 t -2 c_1 \right ) {\mathrm e}^{-2 t}}{4}+\frac {t^{3}}{6}-\frac {t^{2}}{4}+\frac {3 t}{4}+c_2 \]

✓ Solution by Mathematica

Time used: 0.224 (sec). Leaf size: 45

DSolve[D[y[t],{t,2}]+2*D[y[t],t]==1+t^2+Exp[-2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {t^3}{6}-\frac {t^2}{4}+\frac {3 t}{4}-\frac {1}{4} e^{-2 t} (2 t+1+2 c_1)+c_2 \]