Internal problem ID [4027]
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]
\[ \boxed {{y^{\prime }}^{2}-\left (-x +2\right ) y^{\prime }-y=-1} \]
✓ Solution by Maple
Time used: 0.031 (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 \left (x \right ) = -\frac {1}{4} x^{2}+x y \left (x \right ) = c_{1}^{2}+c_{1} x -2 c_{1} +1 \end{align*}
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 29
DSolve[(y'[x])^2-(2-x)y'[x]+1-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x-2)+1+c_1{}^2 y(x)\to -\frac {1}{4} (x-4) x \end{align*}