64.3.2 problem 2

Internal problem ID [13273]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page 37
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 05:13:54 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 58

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

\[ \frac {-i c_{1} \left (x y^{2}+3 x -4 y\right ) \sqrt {3}+12 c_{1} +i}{\left (-\sqrt {3}\, y x +4 \sqrt {3}-3 i x \right ) \left (\sqrt {3}+i y\right )} = 0 \]

✓ Solution by Mathematica

Time used: 0.445 (sec). Leaf size: 79

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

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