Internal problem ID [13880]
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 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y=t} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 4.141 (sec). Leaf size: 24
dsolve([diff(y(t),t$2)-6*diff(y(t),t)+9*y(t)=t,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {2 \,{\mathrm e}^{\frac {3 t}{2}} \left (t \cosh \left (\frac {3 t}{2}\right )-\frac {2 \sinh \left (\frac {3 t}{2}\right )}{3}\right )}{9} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 25
DSolve[{y''[t]-6*y'[t]+9*y[t]==t,{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{27} \left (3 t+e^{3 t} (3 t-2)+2\right ) \]