14.21.15 problem 15

Internal problem ID [2724]
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 : 15
Date solved : Monday, January 27, 2025 at 06:12:21 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 46

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

\[ y = \frac {\left (-t^{4}+48 c_4 t +9 t^{2}+48 c_2 -12\right ) \sin \left (t \right )}{48}-\frac {\cos \left (t \right ) \left (t^{3}+\left (-12 c_3 -3\right ) t -12 c_1 \right )}{12} \]

✓ Solution by Mathematica

Time used: 0.149 (sec). Leaf size: 54

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

\[ y(t)\to \left (-\frac {t^3}{12}+\left (\frac {1}{4}+c_2\right ) t+c_1\right ) \cos (t)+\frac {1}{96} \left (-2 t^4+18 t^2+96 c_4 t-15+96 c_3\right ) \sin (t) \]