60.1.458 problem 471

Internal problem ID [10472]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 471
Date solved : Sunday, March 30, 2025 at 04:51:06 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 33

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

\begin{align*} y &= \sqrt {-x^{2}+c_1} \\ y &= -\sqrt {-x^{2}+c_1} \\ y &= x +c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.125 (sec). Leaf size: 47

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

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

✓ Sympy. Time used: 0.537 (sec). Leaf size: 27

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

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