74.9.3 problem 11

Internal problem ID [16179]
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 : 11
Date solved : Tuesday, January 28, 2025 at 08:56:27 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

dsolve(2*t^2*diff(y(t),t$2)-3*t*diff(y(t),t)-3*y(t)=0,y(t), singsol=all)
 

\[ y = c_{1} t^{3}+\frac {c_{2}}{\sqrt {t}} \]

✓ Solution by Mathematica

Time used: 0.117 (sec). Leaf size: 124

DSolve[2*t^2*D[y[t],{t,2}]-3*D[y[t],t]-3*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \sqrt {\frac {2}{3}} t^{\frac {1}{2}-\frac {\sqrt {7}}{2}} \left (\left (\frac {2}{3}\right )^{\frac {\sqrt {7}}{2}} c_2 t^{\sqrt {7}} \operatorname {Hypergeometric1F1}\left (-\frac {1}{2}-\frac {\sqrt {7}}{2},1-\sqrt {7},-\frac {3}{2 t}\right )+\left (\frac {3}{2}\right )^{\frac {\sqrt {7}}{2}} c_1 \operatorname {Hypergeometric1F1}\left (\frac {1}{2} \left (-1+\sqrt {7}\right ),1+\sqrt {7},-\frac {3}{2 t}\right )\right ) \]