14.21.12 problem 12

Internal problem ID [2721]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.15, Higher order equations. Excercises page 263
Problem number : 12
Date solved : Monday, January 27, 2025 at 06:12:18 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=2 t^{2}+4 \sin \left (t \right ) \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(t),t$3)+diff(y(t),t)=2*t^2+4*sin(t),y(t), singsol=all)
 

\[ y = \left (-c_2 -2\right ) \cos \left (t \right )+\left (c_1 -2 t \right ) \sin \left (t \right )+\frac {2 t^{3}}{3}-4 t +c_3 \]

✓ Solution by Mathematica

Time used: 0.219 (sec). Leaf size: 35

DSolve[D[y[t],{t,3}]+D[y[t],t]==2*t^2+4*Sin[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {2 t^3}{3}-4 t-(2+c_2) \cos (t)+(-2 t+c_1) \sin (t)+c_3 \]