Internal problem ID [12041]
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]]
\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }=\sin \left (t \right )} \]
✓ 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: 1.636 (sec). Leaf size: 82
DSolve[y'''[t]==2*y''[t]-4*y'[t]+Sin[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{52} \left (8 \sin (t)-12 \cos (t)-13 \left (\sqrt {3} c_1-c_2\right ) e^t \cos \left (\sqrt {3} t\right )+13 c_1 e^t \sin \left (\sqrt {3} t\right )+13 \sqrt {3} c_2 e^t \sin \left (\sqrt {3} t\right )\right )+c_3 \]