75.8.13 problem 211

Internal problem ID [16829]
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
Date solved : Tuesday, January 28, 2025 at 09:34:11 AM
CAS classification : [_quadrature]

\begin{align*} x&={y^{\prime }}^{2}-2 y^{\prime }+2 \end{align*}

✓ Solution by Maple

Time used: 0.057 (sec). Leaf size: 37

dsolve(x=diff(y(x),x)^2-2*diff(y(x),x)+2,y(x), singsol=all)
 

\begin{align*} y &= \frac {\left (-2 x +2\right ) \sqrt {x -1}}{3}+x +c_{1} \\ y &= \frac {\left (2 x -2\right ) \sqrt {x -1}}{3}+x +c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 39

DSolve[x==D[y[x],x]^2-2*D[y[x],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*}