Internal problem ID [4100]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 862.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _dAlembert]
\[ \boxed {x {y^{\prime }}^{2}+\left (a +x -y\right ) y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 63
dsolve(x*diff(y(x),x)^2+(a+x-y(x))*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = a -x -2 \sqrt {-a x} y \left (x \right ) = a -x +2 \sqrt {-a x} y \left (x \right ) = -\frac {\left (c_{1}^{2}+c_{1} \right ) x}{-c_{1} -1}-\frac {a c_{1}}{-c_{1} -1} \end{align*}
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 60
DSolve[x (y'[x])^2+(a+x-y[x])y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (x+\frac {a}{1+c_1}\right ) y(x)\to \left (\sqrt {a}-i \sqrt {x}\right )^2 y(x)\to \left (\sqrt {a}+i \sqrt {x}\right )^2 \end{align*}