Internal problem ID [14561]
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: 55.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-y^{\prime }=-3 t -4 \,{\mathrm e}^{2 t} t^{2}} \] With initial conditions \begin {align*} \left [y \left (0\right ) = -{\frac {7}{2}}, y^{\prime }\left (0\right ) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 40
dsolve([diff(y(t),t$2)-diff(y(t),t)=-3*t-4*t^2*exp(2*t),y(0) = -7/2, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {3}{2}+\left (-2 t^{2}+6 t -7\right ) {\mathrm e}^{2 t}+\frac {3 t^{2}}{2}+3 t +5 \,{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.238 (sec). Leaf size: 42
DSolve[{y''[t]-y'[t]==-3*t-4*t^2*Exp[2*t],{y[0]==0,y'[0]==8/9}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {3 t^2}{2}+e^{2 t} \left (-2 t^2+6 t-7\right )+3 t+\frac {53 e^t}{9}+\frac {10}{9} \]