28.1.30 problem 30

Internal problem ID [4336]
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 : 30
Date solved : Monday, January 27, 2025 at 09:06:00 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 4 y x +3 y^{2}-x +x \left (x +2 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

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

dsolve((4*x*y(x)+3*y(x)^2-x)+x*(x+2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.653 (sec). Leaf size: 80

DSolve[(4*x*y[x]+3*y[x]^2-x)+x*(x+2*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x^4+\sqrt {x^2} \sqrt {x^6+x^5+4 c_1 x}}{2 x^3} \\ y(x)\to -\frac {x}{2}+\frac {\sqrt {x^2} \sqrt {x^6+x^5+4 c_1 x}}{2 x^3} \\ \end{align*}