Internal problem ID [14467]
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: 34.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {t^{2} y^{\prime \prime }+3 y^{\prime } t +y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= \frac {1}{t} \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve([t^2*diff(y(t),t$2)+3*t*diff(y(t),t)+y(t)=0,1/t],singsol=all)
\[ y \left (t \right ) = \frac {c_{2} \ln \left (t \right )+c_{1}}{t} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 17
DSolve[t^2*y''[t]+3*t*y'[t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {c_2 \log (t)+c_1}{t} \]