Internal problem ID [14447]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {2 t^{2} y^{\prime \prime }-3 y^{\prime } t -3 y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (t \right ) = c_{1} t^{3}+\frac {c_{2}}{\sqrt {t}} \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 124
DSolve[2*t^2*y''[t]-3*y'[t]-3*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \sqrt {\frac {2}{3}} t^{\frac {1}{2}-\frac {\sqrt {7}}{2}} \left (\left (\frac {2}{3}\right )^{\frac {\sqrt {7}}{2}} c_2 t^{\sqrt {7}} \operatorname {Hypergeometric1F1}\left (-\frac {1}{2}-\frac {\sqrt {7}}{2},1-\sqrt {7},-\frac {3}{2 t}\right )+\left (\frac {3}{2}\right )^{\frac {\sqrt {7}}{2}} c_1 \operatorname {Hypergeometric1F1}\left (\frac {1}{2} \left (-1+\sqrt {7}\right ),1+\sqrt {7},-\frac {3}{2 t}\right )\right ) \]