30.6.6 problem 7

Internal problem ID [7541]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Review problems. page 79
Problem number : 7
Date solved : Tuesday, September 30, 2025 at 04:45:08 PM
CAS classification : [_separable]

\begin{align*} t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 105

ode:=t^3*y(t)^2+t^4/y(t)^6*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= \frac {1}{\left (c_1 +7 \ln \left (t \right )\right )^{{1}/{7}}} \\ y &= -\frac {\left (-1\right )^{{1}/{7}}}{\left (c_1 +7 \ln \left (t \right )\right )^{{1}/{7}}} \\ y &= \frac {\left (-1\right )^{{6}/{7}}}{\left (c_1 +7 \ln \left (t \right )\right )^{{1}/{7}}} \\ y &= -\frac {\left (-1\right )^{{5}/{7}}}{\left (c_1 +7 \ln \left (t \right )\right )^{{1}/{7}}} \\ y &= \frac {\left (-1\right )^{{2}/{7}}}{\left (c_1 +7 \ln \left (t \right )\right )^{{1}/{7}}} \\ y &= -\frac {\left (-1\right )^{{3}/{7}}}{\left (c_1 +7 \ln \left (t \right )\right )^{{1}/{7}}} \\ y &= \frac {\left (-1\right )^{{4}/{7}}}{\left (c_1 +7 \ln \left (t \right )\right )^{{1}/{7}}} \\ \end{align*}

✓ Mathematica. Time used: 0.114 (sec). Leaf size: 183

ode=t^3*y[t]^2+t^4/(y[t]^6)*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {\sqrt [7]{-\frac {1}{7}}}{\sqrt [7]{\log (t)-c_1}}\\ y(t)&\to \frac {1}{\sqrt [7]{7} \sqrt [7]{\log (t)-c_1}}\\ y(t)&\to \frac {(-1)^{2/7}}{\sqrt [7]{7} \sqrt [7]{\log (t)-c_1}}\\ y(t)&\to -\frac {(-1)^{3/7}}{\sqrt [7]{7} \sqrt [7]{\log (t)-c_1}}\\ y(t)&\to \frac {(-1)^{4/7}}{\sqrt [7]{7} \sqrt [7]{\log (t)-c_1}}\\ y(t)&\to -\frac {(-1)^{5/7}}{\sqrt [7]{7} \sqrt [7]{\log (t)-c_1}}\\ y(t)&\to \frac {(-1)^{6/7}}{\sqrt [7]{7} \sqrt [7]{\log (t)-c_1}}\\ y(t)&\to 0 \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**4*Derivative(y(t), t)/y(t)**6 + t**3*y(t)**2,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out