Internal problem ID [13537]
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 (i).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=t^{2} {\mathrm e}^{4 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.079 (sec). Leaf size: 27
dsolve([diff(y(t),t$2)-5*diff(y(t),t)+6*y(t)=t^2*exp(4*t),y(0) = 0, D(y)(0) = 2],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {7 \,{\mathrm e}^{2 t}}{4}+\frac {\left (2 t^{2}-6 t +7\right ) {\mathrm e}^{4 t}}{4} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 32
DSolve[{y''[t]-5*y'[t]+6*y[t]==t^2*Exp[4*t],{y[0]==0,y'[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} e^{2 t} \left (e^{2 t} \left (2 t^2-6 t+7\right )-7\right ) \]