Internal problem ID [6505]
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]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }-5 y=1} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 1.953 (sec). Leaf size: 34
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)
\[ y \left (t \right ) = \frac {13 \,{\mathrm e}^{-\frac {3 t}{2}} \sqrt {29}\, \sinh \left (\frac {t \sqrt {29}}{2}\right )}{145}+\frac {{\mathrm e}^{-\frac {3 t}{2}} \cosh \left (\frac {t \sqrt {29}}{2}\right )}{5}-\frac {1}{5} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 67
DSolve[{y''[t]+3*y'[t]-5*y[t]==1,{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{290} e^{-\frac {1}{2} \left (3+\sqrt {29}\right ) t} \left (\left (29+13 \sqrt {29}\right ) e^{\sqrt {29} t}-58 e^{\frac {1}{2} \left (3+\sqrt {29}\right ) t}+29-13 \sqrt {29}\right ) \]