68.7.10 problem 10

Internal problem ID [17374]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 10
Date solved : Thursday, October 02, 2025 at 02:14:43 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

\[ \frac {1}{\sqrt {y}}+\frac {t^{3}}{7}-\frac {c_1}{\sqrt {t}} = 0 \]

✓ Mathematica. Time used: 0.097 (sec). Leaf size: 25

ode=D[y[t],t]-1/t*y[t]==t^2*y[t]^(3/2); 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {49 t}{\left (t^{7/2}-7 c_1\right ){}^2}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.175 (sec). Leaf size: 22

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

\[ y{\left (t \right )} = \frac {49 t}{49 C_{1}^{2} - 14 C_{1} t^{\frac {7}{2}} + t^{7}} \]