Internal problem ID [5747]
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 The Unit Step and Impulse Functions. Page
303
Problem number: 1(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }-6 y-t=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve([diff(y(t),t$2)+diff(y(t),t)-6*y(t)=t,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = -\frac {\left (-9 \,{\mathrm e}^{5 t}+30 t \,{\mathrm e}^{3 t}+5 \,{\mathrm e}^{3 t}+4\right ) {\mathrm e}^{-3 t}}{180} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 28
DSolve[{y''[t]+y'[t]-6*y[t]==t,{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{180} \left (-30 t-4 e^{-3 t}+9 e^{2 t}-5\right ) \\ \end{align*}