Internal problem ID [14863]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 42.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-4 y=t} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve([diff(y(t),t$2)-4*y(t)=t,y(0) = 2, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {17 \,{\mathrm e}^{2 t}}{16}+\frac {15 \,{\mathrm e}^{-2 t}}{16}-\frac {t}{4} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 16
DSolve[{y''[t]-4*y[t]==0,{y[0]==2,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-2 t}+e^{2 t} \]