28.1.22 problem 22

Internal problem ID [4328]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 22
Date solved : Monday, January 27, 2025 at 09:03:22 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 89

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

\begin{align*} y \left (x \right ) &= \frac {2 x +\sqrt {-x^{4}-6 x^{3}+\left (-2 c_{1} +6\right ) x^{2}+12 x +4 c_{1}}}{x^{2}-2} \\ y \left (x \right ) &= \frac {2 x -\sqrt {-x^{4}-6 x^{3}+\left (-2 c_{1} +6\right ) x^{2}+12 x +4 c_{1}}}{x^{2}-2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.548 (sec). Leaf size: 95

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

\begin{align*} y(x)\to \frac {2 x-\sqrt {-x^4-6 x^3+(6+c_1) x^2+12 x-2 c_1}}{x^2-2} \\ y(x)\to \frac {2 x+\sqrt {-x^4-6 x^3+(6+c_1) x^2+12 x-2 c_1}}{x^2-2} \\ \end{align*}