Internal problem ID [14548]
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: 42.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }=t^{2}-{\mathrm e}^{3 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(t),t$2)-3*diff(y(t),t)=t^2-exp(3*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (1-3 t +3 c_{1} \right ) {\mathrm e}^{3 t}}{9}-\frac {t^{3}}{9}-\frac {t^{2}}{9}-\frac {2 t}{27}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.177 (sec). Leaf size: 42
DSolve[y''[t]-3*y'[t]==t^2-Exp[3*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{27} \left (-3 t^3-3 t^2-2 t+e^{3 t} (-9 t+3+9 c_1)+27 c_2\right ) \]