Internal problem ID [14523]
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: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=t^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(t),t$2)-2*diff(y(t),t)+y(t)=t^2,y(t), singsol=all)
\[ y \left (t \right ) = \left (c_{1} t +c_{2} \right ) {\mathrm e}^{t}+t^{2}+4 t +6 \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 26
DSolve[y''[t]-2*y'[t]+y[t]==t^2,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to t^2+t \left (4+c_2 e^t\right )+c_1 e^t+6 \]