14.11.1 problem 1

Internal problem ID [2594]
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 : 1
Date solved : Monday, January 27, 2025 at 06:01:36 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+3 y&=t^{3}-1 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 30

dsolve(diff(y(t),t$2)+3*y(t)=t^3-1,y(t), singsol=all)
 

\[ y = \sin \left (\sqrt {3}\, t \right ) c_2 +\cos \left (\sqrt {3}\, t \right ) c_1 +\frac {t^{3}}{3}-\frac {2 t}{3}-\frac {1}{3} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 40

DSolve[D[y[t],{t,2}]+3*y[t]==t^3-1,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{3} \left (t^3-2 t-1\right )+c_1 \cos \left (\sqrt {3} t\right )+c_2 \sin \left (\sqrt {3} t\right ) \]