72.16.20 problem 21

Internal problem ID [14916]
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
Date solved : Tuesday, January 28, 2025 at 07:20:16 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=5 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.018 (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)
 

\[ y = -\frac {5 \,{\mathrm e}^{t}}{3}+\frac {5 \,{\mathrm e}^{4 t}}{12}+\frac {5}{4} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 21

DSolve[{D[y[t],{t,2}]-5*D[y[t],t]+4*y[t]==5,{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {5}{12} \left (-4 e^t+e^{4 t}+3\right ) \]