Internal problem ID [13163]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 4. Forcing and Resonance. Section 4.1 page 399
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-2 y=5 \,{\mathrm e}^{3 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(t),t$2)-diff(y(t),t)-2*y(t)=5*exp(3*t),y(t), singsol=all)
\[ y \left (t \right ) = c_{2} {\mathrm e}^{-t}+c_{1} {\mathrm e}^{2 t}+\frac {5 \,{\mathrm e}^{3 t}}{4} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 31
DSolve[y''[t]-y'[t]-2*y[t]==5*Exp[3*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {5 e^{3 t}}{4}+c_1 e^{-t}+c_2 e^{2 t} \]