Internal problem ID [6511]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 7. Laplace Transforms. Section 7.5 Problesm for review and discovery. Section
A, Drill exercises. Page 309
Problem number: 4(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y^{\prime }+2 y=t} \]
✓ Solution by Maple
Time used: 2.0 (sec). Leaf size: 52
dsolve(diff(y(t),t$2)+diff(y(t),t)+2*y(t)=t,y(t), singsol=all)
\[ y \left (t \right ) = -\frac {1}{4}+\frac {t}{2}+\frac {\left (7 \cos \left (\frac {\sqrt {7}\, t}{2}\right ) \left (1+4 y \left (0\right )\right )+\sin \left (\frac {\sqrt {7}\, t}{2}\right ) \sqrt {7}\, \left (8 D\left (y \right )\left (0\right )+4 y \left (0\right )-3\right )\right ) {\mathrm e}^{-\frac {t}{2}}}{28} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 56
DSolve[y''[t]+y'[t]+2*y[t]==t,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {t}{2}+c_2 e^{-t/2} \cos \left (\frac {\sqrt {7} t}{2}\right )+c_1 e^{-t/2} \sin \left (\frac {\sqrt {7} t}{2}\right )-\frac {1}{4} \]