36.1.7 problem 7

Internal problem ID [6262]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 7
Date solved : Wednesday, March 05, 2025 at 12:27:51 AM
CAS classification : [_separable]

\begin{align*} x y^{\prime }&=\frac {1}{y^{3}} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 51

ode:=x*diff(y(x),x) = 1/y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \left (4 \ln \left (x \right )+c_{1} \right )^{{1}/{4}} \\ y &= -\left (4 \ln \left (x \right )+c_{1} \right )^{{1}/{4}} \\ y &= -i \left (4 \ln \left (x \right )+c_{1} \right )^{{1}/{4}} \\ y &= i \left (4 \ln \left (x \right )+c_{1} \right )^{{1}/{4}} \\ \end{align*}

✓ Mathematica. Time used: 0.159 (sec). Leaf size: 84

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

\begin{align*} y(x)\to -\sqrt {2} \sqrt [4]{\log (x)+c_1} \\ y(x)\to -i \sqrt {2} \sqrt [4]{\log (x)+c_1} \\ y(x)\to i \sqrt {2} \sqrt [4]{\log (x)+c_1} \\ y(x)\to \sqrt {2} \sqrt [4]{\log (x)+c_1} \\ \end{align*}

✓ Sympy. Time used: 1.176 (sec). Leaf size: 54

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - 1/y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - i \sqrt [4]{C_{1} + 4 \log {\left (x \right )}}, \ y{\left (x \right )} = i \sqrt [4]{C_{1} + 4 \log {\left (x \right )}}, \ y{\left (x \right )} = - \sqrt [4]{C_{1} + 4 \log {\left (x \right )}}, \ y{\left (x \right )} = \sqrt [4]{C_{1} + 4 \log {\left (x \right )}}\right ] \]