68.9.7 problem 15

Internal problem ID [17470]
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 : Thursday, October 02, 2025 at 02:24:28 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 3 t^{2} y^{\prime \prime }-5 t y^{\prime }-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*}

✓ Maple. Time used: 0.063 (sec). Leaf size: 15

ode:=3*t^2*diff(diff(y(t),t),t)-5*t*diff(y(t),t)-3*y(t) = 0; 
ic:=[y(1) = 1, D(y)(1) = 17/3]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 22

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

\begin{align*} y(t)&\to \frac {9 t^3}{5}-\frac {4}{5 \sqrt [3]{t}} \end{align*}

✓ Sympy. Time used: 0.111 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*t**2*Derivative(y(t), (t, 2)) - 5*t*Derivative(y(t), t) - 3*y(t),0) 
ics = {y(1): 1, Subs(Derivative(y(t), t), t, 1): 17/3} 
dsolve(ode,func=y(t),ics=ics)
 

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