76.12.12 problem 23

Internal problem ID [17568]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
Problem number : 23
Date solved : Tuesday, January 28, 2025 at 10:44:13 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 12

dsolve(diff(y(t),t$2)-2*diff(y(t),t)+y(t)=0,y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 16

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

\[ y(t)\to e^t (c_2 t+c_1) \]