74.2.9 problem 14

Internal problem ID [15850]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Review exercises, page 23
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 08:09:38 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x -3 y+\left (2 y-3 x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.141 (sec). Leaf size: 53

dsolve((2*x-3*y(x))+(2*y(x)-3*x)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {3 c_{1} x -\sqrt {5 c_{1}^{2} x^{2}+4}}{2 c_{1}} \\ y &= \frac {3 c_{1} x +\sqrt {5 c_{1}^{2} x^{2}+4}}{2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.405 (sec). Leaf size: 110

DSolve[(2*x-3*y[x])+(2*y[x]-3*x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} \left (3 x-\sqrt {5 x^2+4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (3 x+\sqrt {5 x^2+4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (3 x-\sqrt {5} \sqrt {x^2}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {5} \sqrt {x^2}+3 x\right ) \\ \end{align*}