Internal problem ID [14090]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {t^{2} y^{\prime \prime }-12 y^{\prime } t +42 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (t \right ) = -t^{7}+t^{6} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 13
DSolve[{t^2*y''[t]-12*t*y'[t]+42*y[t]==0,{y[1]==0,y'[1]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\left ((t-1) t^6\right ) \]