Internal problem ID [644]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation ,
page 164
Problem number: 36.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }+4 t y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(t^2*diff(y(t),t$2)+ 4*t*diff(y(t),t)+2*y(t) = 0,y(t), singsol=all)
\[ y \relax (t ) = \frac {c_{1}}{t^{2}}+\frac {c_{2}}{t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 34
DSolve[t^2*y''[t]+4*t*y'[t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t^{-\frac {3}{2}-\frac {\sqrt {5}}{2}} \left (c_2 t^{\sqrt {5}}+c_1\right ) \\ \end{align*}