Internal problem ID [14832]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
\[ \boxed {t y^{\prime \prime }+2 y^{\prime }+t y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= \frac {\sin \left (t \right )}{t} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([t*diff(y(t),t$2)+2*diff(y(t),t)+t*y(t)=0,sin(t)/t],singsol=all)
\[ y \left (t \right ) = \frac {c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right )}{t} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 37
DSolve[t*y''[t]+2*y'[t]+t*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {2 c_1 e^{-i t}-i c_2 e^{i t}}{2 t} \]