Internal problem ID [4071]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 29
Problem number: 832.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {2 {y^{\prime }}^{2}-\left (1-x \right ) y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 22
dsolve(2*diff(y(x),x)^2-(1-x)*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {\left (x -1\right )^{2}}{8} \\ y \left (x \right ) &= c_{1} \left (2 c_{1} +x -1\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 28
DSolve[2 (y'[x])^2-(1-x)y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x-1+2 c_1) \\ y(x)\to -\frac {1}{8} (x-1)^2 \\ \end{align*}