74.1.46 problem 53

Internal problem ID [15826]
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 : Tuesday, January 28, 2025 at 08:08:19 AM
CAS classification : [[_Emden, _Fowler]]

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

With initial conditions

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

✓ Solution by Maple

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

dsolve([t^2*diff(y(t),t$2)-12*t*diff(y(t),t)+42*y(t)=0,y(1) = 0, D(y)(1) = -1],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 13

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

\[ y(t)\to -\left ((t-1) t^6\right ) \]