Internal problem ID [14471]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number: 45.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {t y^{\prime \prime }+2 y^{\prime }+16 t y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= \frac {\sin \left (4 t \right )}{t} \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve([t*diff(y(t),t$2)+2*diff(y(t),t)+16*t*y(t)=0,1/t*sin(4*t)],singsol=all)
\[ y \left (t \right ) = \frac {c_{1} \sin \left (4 t \right )+c_{2} \cos \left (4 t \right )}{t} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 37
DSolve[t*y''[t]+2*y'[t]+16*t*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {8 c_1 e^{-4 i t}-i c_2 e^{4 i t}}{8 t} \]