74.4.10 problem 10
Internal
problem
ID
[15832]
Book
:
INTRODUCTORY
DIFFERENTIAL
EQUATIONS.
Martha
L.
Abell,
James
P.
Braselton.
Fourth
edition
2014.
ElScAe.
2014
Section
:
Chapter
2.
First
Order
Equations.
Exercises
2.2,
page
39
Problem
number
:
10
Date
solved
:
Monday, March 31, 2025 at 01:57:27 PM
CAS
classification
:
[_separable]
\begin{align*} \frac {3}{t^{2}}&=\left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime } \end{align*}
✓ Maple. Time used: 0.001 (sec). Leaf size: 20
ode:=3/t^2 = (1/y(t)^(1/2)+y(t)^(1/2))*diff(y(t),t);
dsolve(ode,y(t), singsol=all);
\[
-\frac {1}{t}-\frac {2 \sqrt {y}\, \left (y+3\right )}{9}+c_1 = 0
\]
✓ Mathematica. Time used: 6.48 (sec). Leaf size: 445
ode=3/t^2==(1/y[t]^(1/2)+y[t]^(1/2))*D[y[t],t];
ic={};
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
\begin{align*}
y(t)\to \frac {\left (-2+\sqrt [3]{\frac {81}{t^2}+3 \sqrt {\frac {(-3+c_1 t){}^2 \left (\left (16+9 c_1{}^2\right ) t^2-54 c_1 t+81\right )}{t^4}}-\frac {54 c_1}{t}+8+9 c_1{}^2}\right ){}^2}{2 \sqrt [3]{\frac {81}{t^2}+3 \sqrt {\frac {(-3+c_1 t){}^2 \left (\left (16+9 c_1{}^2\right ) t^2-54 c_1 t+81\right )}{t^4}}-\frac {54 c_1}{t}+8+9 c_1{}^2}} \\
y(t)\to \frac {1}{4} i \left (\sqrt {3}+i\right ) \sqrt [3]{\frac {81}{t^2}+3 \sqrt {\frac {(-3+c_1 t){}^2 \left (\left (16+9 c_1{}^2\right ) t^2-54 c_1 t+81\right )}{t^4}}-\frac {54 c_1}{t}+8+9 c_1{}^2}+\frac {-1-i \sqrt {3}}{\sqrt [3]{\frac {81}{t^2}+3 \sqrt {\frac {(-3+c_1 t){}^2 \left (\left (16+9 c_1{}^2\right ) t^2-54 c_1 t+81\right )}{t^4}}-\frac {54 c_1}{t}+8+9 c_1{}^2}}-2 \\
y(t)\to -\frac {1}{4} i \left (\sqrt {3}-i\right ) \sqrt [3]{\frac {81}{t^2}+3 \sqrt {\frac {(-3+c_1 t){}^2 \left (\left (16+9 c_1{}^2\right ) t^2-54 c_1 t+81\right )}{t^4}}-\frac {54 c_1}{t}+8+9 c_1{}^2}+\frac {-1+i \sqrt {3}}{\sqrt [3]{\frac {81}{t^2}+3 \sqrt {\frac {(-3+c_1 t){}^2 \left (\left (16+9 c_1{}^2\right ) t^2-54 c_1 t+81\right )}{t^4}}-\frac {54 c_1}{t}+8+9 c_1{}^2}}-2 \\
\end{align*}
✗ Sympy
from sympy import *
t = symbols("t")
y = Function("y")
ode = Eq((-sqrt(y(t)) - 1/sqrt(y(t)))*Derivative(y(t), t) + 3/t**2,0)
ics = {}
dsolve(ode,func=y(t),ics=ics)
Timed Out