Internal problem ID [4114]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 877.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _dAlembert]
\[ \boxed {\left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 59
dsolve((1+x)*diff(y(x),x)^2-(x+y(x))*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = x +2-2 \sqrt {x +1} y \left (x \right ) = x +2+2 \sqrt {x +1} y \left (x \right ) = \frac {\left (-c_{1}^{2}+c_{1} \right ) x}{1-c_{1}}-\frac {c_{1}^{2}}{1-c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 51
DSolve[(1+x) (y'[x])^2-(x+y[x])y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (x+\frac {c_1}{-1+c_1}\right ) y(x)\to x-2 \sqrt {x+1}+2 y(x)\to x+2 \sqrt {x+1}+2 \end{align*}