Internal problem ID [3505]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 27
Problem number: 773.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-2 y^{\prime }+a \left (x -y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 42
dsolve(diff(y(x),x)^2-2*diff(y(x),x)+a*(x-y(x)) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {a x -1}{a} \\ y \relax (x ) = x +\frac {\frac {\left (c_{1}-x \right )^{2} a^{2}}{4}+\left (c_{1}-x \right ) a}{a} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.279 (sec). Leaf size: 84
DSolve[(y'[x])^2-2 y'[x]+a(x-y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} a \left (x^2-2 \sqrt {2} c_1 x+2 c_1{}^2\right )-\frac {1}{a}+x \\ y(x)\to \frac {1}{4} a \left (x^2+2 \sqrt {2} c_1 x+2 c_1{}^2\right )-\frac {1}{a}+x \\ y(x)\to x-\frac {1}{a} \\ \end{align*}