Internal problem ID [14452]
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: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {t^{2} y^{\prime \prime }+7 y^{\prime } t -7 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 2, y^{\prime }\left (1\right ) = -22] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 13
dsolve([t^2*diff(y(t),t$2)+7*t*diff(y(t),t)-7*y(t)=0,y(1) = 2, D(y)(1) = -22],y(t), singsol=all)
\[ y \left (t \right ) = \frac {3}{t^{7}}-t \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 14
DSolve[{t^2*y''[t]+7*t*y'[t]-7*y[t]==0,{y[1]==2,y'[1]==-22}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {3}{t^7}-t \]