Internal problem ID [646]
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: 38.
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 }-6 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)-6*y(t) = 0,y(t), singsol=all)
\[ y \relax (t ) = \frac {c_{1}}{t}+c_{2} t^{6} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[t^2*y''[t]-4*t*y'[t]-6*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {c_2 t^7+c_1}{t} \\ \end{align*}