74.9.8 problem 16

Internal problem ID [16184]
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
Date solved : Tuesday, January 28, 2025 at 08:56:39 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} y^{\prime \prime }+7 y^{\prime } t -7 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=-22 \end{align*}

✓ Solution by Maple

Time used: 0.019 (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)
 

\[ y = \frac {3}{t^{7}}-t \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 14

DSolve[{t^2*D[y[t],{t,2}]+7*t*D[y[t],t]-7*y[t]==0,{y[1]==2,Derivative[1][y][1]==-22}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {3}{t^7}-t \]