Internal problem ID [13883]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 29. Convolution. Additional Exercises. page 523
Problem number: 29.7 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y={\mathrm e}^{t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 4.781 (sec). Leaf size: 20
dsolve([diff(y(t),t$2)-6*diff(y(t),t)+9*y(t)=exp(t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{t}}{4}+\frac {\left (2 t -1\right ) {\mathrm e}^{3 t}}{4} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 24
DSolve[{y''[t]-6*y'[t]+9*y[t]==Exp[t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} \left (e^{3 t} (2 t-1)+e^t\right ) \]