Internal problem ID [1742]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime }-4 y^{\prime }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 11
dsolve([4*diff(y(t),t$2)-4*diff(y(t),t)+y(t)=0,y(0) = 0, D(y)(0) = 3],y(t), singsol=all)
\[ y \relax (t ) = 3 t \,{\mathrm e}^{\frac {t}{2}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 15
DSolve[{4*y''[t]-4*y'[t]+y[t]==0,{y[0]==0,y'[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 3 e^{t/2} t \\ \end{align*}