Internal problem ID [12841]
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: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-6 y={\mathrm e}^{4 t}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve(diff(y(t),t$2)-diff(y(t),t)-6*y(t)=exp(4*t),y(t), singsol=all)
\[ y \left (t \right ) = c_{2} {\mathrm e}^{3 t}+c_{1} {\mathrm e}^{-2 t}+\frac {{\mathrm e}^{4 t}}{6} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 31
DSolve[y''[t]-y'[t]-6*y[t]==Exp[4*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {e^{4 t}}{6}+c_1 e^{-2 t}+c_2 e^{3 t} \]