Internal problem ID [14553]
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: 47.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-y=4} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve([diff(y(t),t$2)-y(t)=4,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = 2 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{t}-4 \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 19
DSolve[{y''[t]-y[t]==4,{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 2 e^{-t} \left (e^t-1\right )^2 \]