44.3.23 problem 31

Internal problem ID [7004]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Review problems at page 34
Problem number : 31
Date solved : Monday, January 27, 2025 at 02:40:39 PM
CAS classification : [_separable]

\begin{align*} x y^{\prime }+y&=\frac {1}{y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 59

dsolve(x*diff(y(x),x)+y(x)=1/y(x)^2,y(x), singsol=all)
 

\begin{align*} y &= \frac {\left (x^{3}+c_{1} \right )^{{1}/{3}}}{x} \\ y &= -\frac {\left (x^{3}+c_{1} \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{2 x} \\ y &= \frac {\left (x^{3}+c_{1} \right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.271 (sec). Leaf size: 159

DSolve[x*D[y[x],x]+y[x]==1/y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {\sqrt [3]{x^3+e^{3 c_1}}}{x} \\ y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{x^3+e^{3 c_1}}}{x} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{x^3+e^{3 c_1}}}{x} \\ y(x)\to 1 \\ y(x)\to -\sqrt [3]{-1} \\ y(x)\to (-1)^{2/3} \\ y(x)\to \frac {\sqrt [3]{x^3}}{x} \\ y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{x^3}}{x} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{x^3}}{x} \\ \end{align*}