Internal problem ID [13547]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 28. The inverse Laplace transform. Additional Exercises. page 509
Problem number: 28.8 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y={\mathrm e}^{3 t} t^{2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 13
dsolve([diff(y(t),t$2)-6*diff(y(t),t)+9*y(t)=exp(3*t)*t^2,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {t^{4} {\mathrm e}^{3 t}}{12} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 17
DSolve[{y''[t]-6*y'[t]+9*y[t]==Exp[3*t]*t^2,{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{12} e^{3 t} t^4 \]