Internal problem ID [14536]
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: 30.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }-4 y=-32 t^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
dsolve(diff(y(t),t$2)+3*diff(y(t),t)-4*y(t)=-32*t^2,y(t), singsol=all)
\[ y \left (t \right ) = \left (8 t^{2}+12 t +13\right ) {\mathrm e}^{-4 t} {\mathrm e}^{4 t}+\left (c_{2} {\mathrm e}^{5 t}+c_{1} \right ) {\mathrm e}^{-4 t} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 29
DSolve[y''[t]+3*y'[t]-4*y[t]==-32*t^2,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 8 t^2+12 t+c_1 e^{-4 t}+c_2 e^t+13 \]