Internal problem ID [12848]
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: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-6 y=4 \,{\mathrm e}^{-3 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(t),t$2)+diff(y(t),t)-6*y(t)=4*exp(-3*t),y(t), singsol=all)
\[ y \left (t \right ) = c_{2} {\mathrm e}^{2 t}+c_{1} {\mathrm e}^{-3 t}-\frac {4 \,{\mathrm e}^{-3 t} t}{5} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 32
DSolve[y''[t]+y'[t]-6*y[t]==4*Exp[-3*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{25} e^{-3 t} \left (-20 t+25 c_2 e^{5 t}-4+25 c_1\right ) \]