77.1.46 problem 65 (page 109)

Internal problem ID [17865]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 65 (page 109)
Date solved : Monday, March 31, 2025 at 04:37:37 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 33

ode:=diff(y(x),x)^2*y(x)+diff(y(x),x)*(x-y(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: 0.107 (sec). Leaf size: 47

ode=D[y[x],x]^2*y[x]+D[y[x],x]*(x-y[x])-x==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: 0.582 (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)
 

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