Internal problem ID [12860]
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: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+4 y=5} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve([diff(y(t),t$2)-5*diff(y(t),t)+4*y(t)=5,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {5 \,{\mathrm e}^{t}}{3}+\frac {5 \,{\mathrm e}^{4 t}}{12}+\frac {5}{4} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 21
DSolve[{y''[t]-5*y'[t]+4*y[t]==5,{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {5}{12} \left (-4 e^t+e^{4 t}+3\right ) \]