Internal problem ID [668]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime }+\frac {y}{4}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = b] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \relax (t ) = {\mathrm e}^{\frac {t}{2}} \left (2+t \left (b -1\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 20
DSolve[{y''[t]-y'[t]+25/100*y[t]==0,{y[0]==2,y'[0]==b}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{t/2} ((b-1) t+2) \\ \end{align*}