Internal problem ID [11699]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page
67
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {5 y x +4 y^{2}+\left (2 y x +x^{2}\right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
dsolve((5*x*y(x)+4*y(x)^2+1)+(x^2+2*x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {-x^{3}-\sqrt {x^{6}-x^{4}-4 c_{1}}}{2 x^{2}} \\ y \left (x \right ) &= \frac {-x^{3}+\sqrt {x^{6}-x^{4}-4 c_{1}}}{2 x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.558 (sec). Leaf size: 84
DSolve[(5*x*y[x]+4*y[x]^2+1)+(x^2+2*x*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^5+\sqrt {x^3} \sqrt {x^7-x^5+4 c_1 x}}{2 x^4} \\ y(x)\to -\frac {x}{2}+\frac {\sqrt {x^3} \sqrt {x^7-x^5+4 c_1 x}}{2 x^4} \\ \end{align*}