Internal problem ID [10579]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{2}+3+\left (2 x y-4\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
dsolve((y(x)^2+3)+(2*x*y(x)-4)*diff(y(x),x)=0,y(x), singsol=all)
\[ c_{1} +\frac {1}{\left (i \sqrt {3}-y \left (x \right )\right ) \left (i \left (x y \left (x \right )-4\right ) \sqrt {3}-3 x \right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.392 (sec). Leaf size: 77
DSolve[(y[x]^2+3)+(2*x*y[x]-4)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2-\sqrt {4+x (-3 x+c_1)}}{x} \\ y(x)\to \frac {2+\sqrt {4+x (-3 x+c_1)}}{x} \\ y(x)\to -i \sqrt {3} \\ y(x)\to i \sqrt {3} \\ \end{align*}