72.16.7 problem 7

Internal problem ID [14903]
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 : 7
Date solved : Tuesday, January 28, 2025 at 07:19:27 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 20

dsolve(diff(y(t),t$2)-5*diff(y(t),t)+4*y(t)=exp(4*t),y(t), singsol=all)
 

\[ y = \frac {\left (t +3 c_{1} \right ) {\mathrm e}^{4 t}}{3}+c_{2} {\mathrm e}^{t} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 29

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

\[ y(t)\to c_1 e^t+e^{4 t} \left (\frac {t}{3}-\frac {1}{9}+c_2\right ) \]