68.9.3 problem 11

Internal problem ID [17466]
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 : Thursday, October 02, 2025 at 02:24:24 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \frac {c_1}{\sqrt {t}}+c_2 \,t^{3} \]

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 124

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

\begin{align*} 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 ) \end{align*}

✓ Sympy. Time used: 0.092 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*t**2*Derivative(y(t), (t, 2)) - 3*t*Derivative(y(t), t) - 3*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {C_{1}}{\sqrt {t}} + C_{2} t^{3} \]