60.1.368 problem 377

Internal problem ID [10382]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 377
Date solved : Wednesday, March 05, 2025 at 10:43:07 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} {y^{\prime }}^{2}+\left (x -2\right ) y^{\prime }-y+1&=0 \end{align*}

✓ Maple. Time used: 0.033 (sec). Leaf size: 24

ode:=diff(y(x),x)^2+(x-2)*diff(y(x),x)-y(x)+1 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {1}{4} x^{2}+x \\ y &= 1+c_{1}^{2}+c_{1} \left (x -2\right ) \\ \end{align*}

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 29

ode=1 - y[x] + (-2 + x)*D[y[x],x] + D[y[x],x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 (x-2)+1+c_1{}^2 \\ y(x)\to -\frac {1}{4} (x-4) x \\ \end{align*}

✓ Sympy. Time used: 1.691 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x - 2)*Derivative(y(x), x) - y(x) + Derivative(y(x), x)**2 + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}^{2}}{4} + \frac {C_{1} x}{2} + x \]