Internal problem ID [5752]
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: 3(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }-5 y-1=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 40
dsolve([diff(y(t),t$2)+3*diff(y(t),t)-5*y(t)=1,y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (29+13 \sqrt {29}\right ) {\mathrm e}^{\frac {\left (-3+\sqrt {29}\right ) t}{2}}}{290}-\frac {1}{5}+\frac {\left (29-13 \sqrt {29}\right ) {\mathrm e}^{-\frac {\left (3+\sqrt {29}\right ) t}{2}}}{290} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 52
DSolve[{y''[t]+3*y'[t]-5*y[t]==1,{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{145} e^{-3 t/2} \left (13 \sqrt {29} \sinh \left (\frac {\sqrt {29} t}{2}\right )+29 \cosh \left (\frac {\sqrt {29} t}{2}\right )\right )-\frac {1}{5} \\ \end{align*}