Internal problem ID [4013]
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]
\[ \boxed {{y^{\prime }}^{2}-2 y^{\prime }+a \left (-y+x \right )=0} \]
✓ Solution by Maple
Time used: 0.047 (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 \left (x \right ) = \frac {a x -1}{a} y \left (x \right ) = 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: 0.466 (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*}