Internal problem ID [10582]
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: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {6 x y+2 y^{2}-5+\left (3 x^{2}+4 x y-6\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 67
dsolve((6*x*y(x)+2*y(x)^2-5)+(3*x^2+4*x*y(x)-6)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {-3 x^{2}+6+\sqrt {9 x^{4}-8 x c_{1} +4 x^{2}+36}}{4 x} \\ y \left (x \right ) = -\frac {3 x^{2}+\sqrt {9 x^{4}-8 x c_{1} +4 x^{2}+36}-6}{4 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.471 (sec). Leaf size: 79
DSolve[(6*x*y[x]+2*y[x]^2-5)+(3*x^2+4*x*y[x]-6)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {3 x^2+\sqrt {9 x^4+4 x^2+16 c_1 x+36}-6}{4 x} \\ y(x)\to \frac {-3 x^2+\sqrt {9 x^4+4 x^2+16 c_1 x+36}+6}{4 x} \\ \end{align*}