44.2.23 problem 23

Internal problem ID [6955]
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. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 23
Date solved : Monday, January 27, 2025 at 02:38:18 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} \left (x^{2}+y^{2}\right ) y^{\prime }&=y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.056 (sec). Leaf size: 42

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

\[ y = {\mathrm e}^{\frac {2 \sqrt {3}\, \operatorname {RootOf}\left (-2 \sqrt {3}\, {\mathrm e}^{\frac {2 \sqrt {3}\, \textit {\_Z}}{3}-c_{1}}+\sqrt {3}\, x -3 x \tan \left (\textit {\_Z} \right )\right )}{3}-c_{1}} \]

✓ Solution by Mathematica

Time used: 0.130 (sec). Leaf size: 42

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

\[ \text {Solve}\left [\frac {2 \arctan \left (\frac {\frac {2 y(x)}{x}-1}{\sqrt {3}}\right )}{\sqrt {3}}+\log \left (\frac {y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]