Internal problem ID [2592]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 10, page 47
Problem number: 2(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y x -1+\left (x^{2}-y x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve((x*y(x)-1)+(x^2-x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = x -\sqrt {x^{2}-2 \ln \relax (x )+2 c_{1}} \\ y \relax (x ) = x +\sqrt {x^{2}-2 \ln \relax (x )+2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.469 (sec). Leaf size: 68
DSolve[(x*y[x]-1)+(x^2-x*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\sqrt {-\frac {1}{x}} \sqrt {-x \left (x^2-2 \log (x)+c_1\right )} \\ y(x)\to x+x \left (-\frac {1}{x}\right )^{3/2} \sqrt {-x \left (x^2-2 \log (x)+c_1\right )} \\ \end{align*}