Internal problem ID [10580]
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: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]
\[ \boxed {2 x y+1+\left (x^{2}+4 y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 47
dsolve((2*x*y(x)+1)+(x^2+4*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {x^{2}}{4}-\frac {\sqrt {x^{4}-8 c_{1} -8 x}}{4} \\ y \left (x \right ) = -\frac {x^{2}}{4}+\frac {\sqrt {x^{4}-8 c_{1} -8 x}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.133 (sec). Leaf size: 61
DSolve[(2*x*y[x]+1)+(x^2+4*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-x^2-\sqrt {x^4-8 x+16 c_1}\right ) \\ y(x)\to \frac {1}{4} \left (-x^2+\sqrt {x^4-8 x+16 c_1}\right ) \\ \end{align*}