Internal problem ID [11597]
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`]]
\[ \boxed {y^{2}+\left (2 y x -4\right ) y^{\prime }=-3} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 62
dsolve((y(x)^2+3)+(2*x*y(x)-4)*diff(y(x),x)=0,y(x), singsol=all)
\[ \frac {-i c_{1} \left (y \left (x \right )^{2} x +3 x -4 y \left (x \right )\right ) \sqrt {3}+12 c_{1} +i}{\left (-y \left (x \right ) \sqrt {3}\, x +4 \sqrt {3}-3 i x \right ) \left (\sqrt {3}+i y \left (x \right )\right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.615 (sec). Leaf size: 79
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 {-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*}