28.1.21 problem 21

Internal problem ID [4327]
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 : 21
Date solved : Monday, January 27, 2025 at 09:03:20 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 53

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

\begin{align*} y \left (x \right ) &= \frac {-6-\sqrt {12 x^{3}+18 c_{1} +54 x +36}}{3 x} \\ y \left (x \right ) &= \frac {-6+\sqrt {12 x^{3}+18 c_{1} +54 x +36}}{3 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.784 (sec). Leaf size: 87

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

\begin{align*} y(x)\to -\frac {6 x+\sqrt {3} \sqrt {x^2 \left (4 x^3+18 x+12+3 c_1\right )}}{3 x^2} \\ y(x)\to \frac {-6 x+\sqrt {3} \sqrt {x^2 \left (4 x^3+18 x+12+3 c_1\right )}}{3 x^2} \\ \end{align*}