Internal problem ID [14464]
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: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {t^{2} y^{\prime \prime }+4 y^{\prime } t -4 y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= \frac {1}{t^{4}} \end {align*}
✓ 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)-4*y(t)=0,1/t^4],singsol=all)
\[ y \left (t \right ) = \frac {c_{1} t^{5}+c_{2}}{t^{4}} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 16
DSolve[t^2*y''[t]+4*t*y'[t]-4*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {c_1}{t^4}+c_2 t \]