75.8.13 problem 211

Internal problem ID [16758]
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 : Monday, March 31, 2025 at 03:16:11 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 37

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

\begin{align*} y &= \frac {\left (-2 x +2\right ) \sqrt {-1+x}}{3}+x +c_1 \\ y &= \frac {\left (2 x -2\right ) \sqrt {-1+x}}{3}+x +c_1 \\ \end{align*}

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

ode=x==D[y[x],x]^2-2*D[y[x],x]+2; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.211 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x - Derivative(y(x), x)**2 + 2*Derivative(y(x), x) - 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} + x - \frac {2 \left (x - 1\right )^{\frac {3}{2}}}{3}, \ y{\left (x \right )} = C_{1} + x + \frac {2 \left (x - 1\right )^{\frac {3}{2}}}{3}\right ] \]