Internal problem ID [14538]
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: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+8 y=-256 t^{3}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(diff(y(t),t$2)-6*diff(y(t),t)+8*y(t)=-256*t^3,y(t), singsol=all)
\[ y \left (t \right ) = \frac {c_{1} {\mathrm e}^{4 t}}{2}-45-84 t -72 t^{2}-32 t^{3}+c_{2} {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 36
DSolve[y''[t]-6*y'[t]+8*y[t]==-256*t^3,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -32 t^3-72 t^2-84 t+c_1 e^{2 t}+c_2 e^{4 t}-45 \]