Internal problem ID [3590]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 861.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _dAlembert]
\[ \boxed {x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 56
dsolve(x*diff(y(x),x)^2+(x-y(x))*diff(y(x),x)+1-y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -x -2 \sqrt {x} \\ y \left (x \right ) = -x +2 \sqrt {x} \\ y \left (x \right ) = \frac {\left (-c_{1}^{2}-c_{1} \right ) x}{-c_{1} -1}-\frac {1}{-c_{1} -1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 46
DSolve[x (y'[x])^2+(x-y[x])y'[x]+1-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x+\frac {1}{1+c_1} \\ y(x)\to -x-2 \sqrt {x} \\ y(x)\to 2 \sqrt {x}-x \\ \end{align*}