10.9.16 problem 16

Internal problem ID [1318]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page 172
Problem number : 16
Date solved : Monday, January 27, 2025 at 04:50:57 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }+\frac {y}{4}&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=b \end{align*}

✓ Solution by Maple

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

dsolve([diff(y(t),t$2)-diff(y(t),t)+25/100*y(t) = 0,y(0) = 2, D(y)(0) = b],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 20

DSolve[{D[y[t],{t,2}]-D[y[t],t]+25/100*y[t]==0,{y[0]==2,Derivative[1][y][0] ==b}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{t/2} ((b-1) t+2) \]