67.5.11 problem Problem 2(f)

Internal problem ID [14097]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number : Problem 2(f)
Date solved : Tuesday, January 28, 2025 at 06:14:24 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 49

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

\[ y = \frac {{\mathrm e}^{t} \left (-\sqrt {3}\, c_{2} +c_{1} \right ) \cos \left (\sqrt {3}\, t \right )}{4}+\frac {{\mathrm e}^{t} \left (\sqrt {3}\, c_{1} +c_{2} \right ) \sin \left (\sqrt {3}\, t \right )}{4}+c_{3} -\frac {3 \cos \left (t \right )}{13}+\frac {2 \sin \left (t \right )}{13} \]

✓ Solution by Mathematica

Time used: 60.464 (sec). Leaf size: 130

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

\[ y(t)\to \int _1^te^{K[3]} \left (c_2 \cos \left (\sqrt {3} K[3]\right )+\int _1^{K[3]}-\frac {e^{-K[2]} \sin (K[2]) \sin \left (\sqrt {3} K[2]\right )}{\sqrt {3}}dK[2] \cos \left (\sqrt {3} K[3]\right )+c_1 \sin \left (\sqrt {3} K[3]\right )+\sin \left (\sqrt {3} K[3]\right ) \int _1^{K[3]}\frac {e^{-K[1]} \cos \left (\sqrt {3} K[1]\right ) \sin (K[1])}{\sqrt {3}}dK[1]\right )dK[3]+c_3 \]