Internal problem ID [3101]
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`]]
\[ \boxed {y x +\left (x^{2}-y x \right ) y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.015 (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 \left (x \right ) &= x -\sqrt {x^{2}-2 \ln \left (x \right )+2 c_{1}} \\ y \left (x \right ) &= x +\sqrt {x^{2}-2 \ln \left (x \right )+2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.46 (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*}