Internal problem ID [14554]
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: 48.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-4 y=32 t} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 6] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve([diff(y(t),t$2)-4*y(t)=32*t,y(0) = 0, D(y)(0) = 6],y(t), singsol=all)
\[ y \left (t \right ) = \frac {7 \,{\mathrm e}^{2 t}}{2}-\frac {7 \,{\mathrm e}^{-2 t}}{2}-8 t \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 27
DSolve[{y''[t]-4*y[t]==32*t,{y[0]==0,y'[0]==6}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -8 t-\frac {7 e^{-2 t}}{2}+\frac {7 e^{2 t}}{2} \]