Internal problem ID [3519]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 27
Problem number: 787.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-\left (2-x \right ) y^{\prime }+1-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.082 (sec). Leaf size: 25
dsolve(diff(y(x),x)^2-(2-x)*diff(y(x),x)+1-y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {1}{4} x^{2}+x \\ y \relax (x ) = c_{1}^{2}+c_{1} x -2 c_{1}+1 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 27
DSolve[(y'[x])^2-(2-x)y'[x]+1-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1+c_1 (x-2+c_1) \\ y(x)\to -\frac {1}{4} (x-4) x \\ \end{align*}