Internal problem ID [13858]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 27. Differentiation and the Laplace transform. Additional Exercises. page
496
Problem number: 27.1 (j).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=7} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 4.094 (sec). Leaf size: 18
dsolve([diff(y(t),t$2)-5*diff(y(t),t)+6*y(t)=7,y(0) = 2, D(y)(0) = 4],y(t), singsol=all)
\[ y \left (t \right ) = \frac {7 \,{\mathrm e}^{3 t}}{3}-\frac {3 \,{\mathrm e}^{2 t}}{2}+\frac {7}{6} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 25
DSolve[{y''[t]-5*y'[t]+6*y[t]==7,{y[0]==2,y'[0]==4}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{6} \left (-9 e^{2 t}+14 e^{3 t}+7\right ) \]