36.4.6 problem 7
Internal
problem
ID
[6344]
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
:
Sunday, March 30, 2025 at 10:52:57 AM
CAS
classification
:
[_separable]
\begin{align*} t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}}&=0 \end{align*}
✓ Maple. Time used: 0.005 (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: 0.185 (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