26.5.16 problem 20

Internal problem ID [4290]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, End of chapter, page 61
Problem number : 20
Date solved : Monday, January 27, 2025 at 08:49:16 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 59

dsolve((y(x)^2-3*x*y(x)-2*x^2)=(x^2-x*y(x))*diff(y(x),x),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: 0.734 (sec). Leaf size: 99

DSolve[(y[x]^2-3*x*y[x]-2*x^2)==(x^2-x*y[x])*D[y[x],x],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*}