68.1.46 problem 53

Internal problem ID [17113]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 53
Date solved : Thursday, October 02, 2025 at 01:43:21 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} y^{\prime \prime }-12 t y^{\prime }+42 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ y^{\prime }\left (1\right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 13

ode:=t^2*diff(diff(y(t),t),t)-12*t*diff(y(t),t)+42*y(t) = 0; 
ic:=[y(1) = 0, D(y)(1) = -1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -t^{7}+t^{6} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 13

ode=t^2*D[y[t],{t,2}]-12*t*D[y[t],t]+42*y[t]==0; 
ic={y[1]==0,Derivative[1][y][1]==-1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\left ((t-1) t^6\right ) \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*Derivative(y(t), (t, 2)) - 12*t*Derivative(y(t), t) + 42*y(t),0) 
ics = {y(1): 0, Subs(Derivative(y(t), t), t, 1): -1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = t^{6} \left (1 - t\right ) \]