77.1.73 problem 92 (page 135)

Internal problem ID [17892]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 92 (page 135)
Date solved : Monday, March 31, 2025 at 04:48:21 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.038 (sec). Leaf size: 31

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

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

✓ Mathematica. Time used: 60.096 (sec). Leaf size: 1178

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 28.531 (sec). Leaf size: 105

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

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