Internal problem ID [15099]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 8. First order not solved for the derivative. Exercises page 67
Problem number: 211.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {-{y^{\prime }}^{2}+2 y^{\prime }=-x +2} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 37
dsolve(x=diff(y(x),x)^2-2*diff(y(x),x)+2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\left (-2 x +2\right ) \sqrt {-1+x}}{3}+x +c_{1} \\ y \left (x \right ) &= \frac {\left (2 x -2\right ) \sqrt {-1+x}}{3}+x +c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 39
DSolve[x==y'[x]^2-2*y'[x]+2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2}{3} (x-1)^{3/2}+x+c_1 \\ y(x)\to \frac {2}{3} (x-1)^{3/2}+x+c_1 \\ \end{align*}