74.9.8 problem 16

Internal problem ID [16113]
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 : Monday, March 31, 2025 at 02:44:06 PM
CAS classification : [[_Emden, _Fowler]]

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

With initial conditions

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 13

ode:=t^2*diff(diff(y(t),t),t)+7*t*diff(y(t),t)-7*y(t) = 0; 
ic:=y(1) = 2, D(y)(1) = -22; 
dsolve([ode,ic],y(t), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.160 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*Derivative(y(t), (t, 2)) + 7*t*Derivative(y(t), t) - 7*y(t),0) 
ics = {y(1): 2, Subs(Derivative(y(t), t), t, 1): -22} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - t + \frac {3}{t^{7}} \]