74.9.7 problem 15

Internal problem ID [16183]
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 : 15
Date solved : Tuesday, January 28, 2025 at 08:56:36 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 3 t^{2} y^{\prime \prime }-5 y^{\prime } t -3 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1\\ y^{\prime }\left (1\right )&={\frac {17}{3}} \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 15

dsolve([3*t^2*diff(y(t),t$2)-5*t*diff(y(t),t)-3*y(t)=0,y(1) = 1, D(y)(1) = 17/3],y(t), singsol=all)
 

\[ y = -\frac {4}{5 t^{{1}/{3}}}+\frac {9 t^{3}}{5} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 22

DSolve[{3*t^2*D[y[t],{t,2}]-5*t*D[y[t],t]-3*y[t]==0,{y[1]==1,Derivative[1][y][1]==17/3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {9 t^3}{5}-\frac {4}{5 \sqrt [3]{t}} \]