Internal problem ID [14562]
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: 56.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }=2 t^{2}} \] With initial conditions \begin {align*} \left [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = {\frac {3}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve([diff(y(t),t$2)-2*diff(y(t),t)=2*t^2,y(0) = 3, D(y)(0) = 3/2],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{2 t}-\frac {t^{2}}{2}-\frac {t^{3}}{3}-\frac {t}{2}+2 \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 30
DSolve[{y''[t]-2*y'[t]==2*t^2,{y[0]==3,y'[0]==3/2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{6} \left (-2 t^3-3 t^2-3 t+12\right )+e^{2 t} \]