Internal problem ID [11013]
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).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-\sin \left (t \right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 64
dsolve(diff(y(t),t$3)=2*diff(y(t),t$2)-4*diff(y(t),t)+sin(t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{t} \cos \left (\sqrt {3}\, t \right ) c_{1}}{4}+\frac {c_{1} \sqrt {3}\, {\mathrm e}^{t} \sin \left (\sqrt {3}\, t \right )}{4}-\frac {c_{2} \sqrt {3}\, {\mathrm e}^{t} \cos \left (\sqrt {3}\, t \right )}{4}+\frac {{\mathrm e}^{t} \sin \left (\sqrt {3}\, t \right ) c_{2}}{4}+\frac {2 \sin \left (t \right )}{13}-\frac {3 \cos \left (t \right )}{13}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.485 (sec). Leaf size: 69
DSolve[y'''[t]==2*y''[t]-4*y'[t]+Sin[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {2 \sin (t)}{13}-\frac {3 \cos (t)}{13}+\frac {1}{4} e^t \left (\left (c_2-\sqrt {3} c_1\right ) \cos \left (\sqrt {3} t\right )+\left (c_1+\sqrt {3} c_2\right ) \sin \left (\sqrt {3} t\right )\right )+c_3 \\ \end{align*}