32.6.29 problem Exercise 12.29, page 103

Internal problem ID [5894]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.29, page 103
Date solved : Monday, January 27, 2025 at 01:25:03 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 59

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

\begin{align*} y \left (x \right ) &= \frac {c_{1} x^{2}-\sqrt {2 c_{1}^{2} x^{4}+1}}{c_{1} x} \\ y \left (x \right ) &= \frac {c_{1} x^{2}+\sqrt {2 c_{1}^{2} x^{4}+1}}{c_{1} x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.749 (sec). Leaf size: 99

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

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