76.15.11 problem 11

Internal problem ID [17652]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.5 (Nonhomogeneous Equations, Method of Undetermined Coefficients). Problems at page 260
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 10:47:32 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&=t^{2}+3 \sin \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 33

dsolve(2*diff(y(t),t$2)+3*diff(y(t),t)+y(t)=t^2+3*sin(t),y(t), singsol=all)
 

\[ y = -2 \,{\mathrm e}^{-t} c_{1} +14-6 t +t^{2}-\frac {9 \cos \left (t \right )}{10}-\frac {3 \sin \left (t \right )}{10}+c_{2} {\mathrm e}^{-\frac {t}{2}} \]

✓ Solution by Mathematica

Time used: 0.112 (sec). Leaf size: 43

DSolve[2*D[y[t],{t,2}]+3*D[y[t],t]+y[t]==t^2+3*Sin[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t^2-6 t-\frac {3 \sin (t)}{10}-\frac {9 \cos (t)}{10}+c_1 e^{-t/2}+c_2 e^{-t}+14 \]