Internal problem ID [14556]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number: 50.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-6 y=3 t} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {23}{12}}, y^{\prime }\left (0\right ) = -{\frac {3}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(y(t),t$2)+diff(y(t),t)-6*y(t)=3*t,y(0) = 23/12, D(y)(0) = -3/2],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\left (\left (t +\frac {1}{6}\right ) {\mathrm e}^{3 t}-2 \,{\mathrm e}^{5 t}-2\right ) {\mathrm e}^{-3 t}}{2} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 24
DSolve[{y''[t]+y'[t]-6*y[t]==3*t,{y[0]==23/12,y'[0]==-3/2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {t}{2}+e^{-3 t}+e^{2 t}-\frac {1}{12} \]