60.1.275 problem 281

Internal problem ID [10289]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 281
Date solved : Sunday, March 30, 2025 at 03:43:25 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.139 (sec). Leaf size: 55

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

\begin{align*} y &= \frac {1-\sqrt {-4 c_1^{2} x^{2}+4 c_1 x +1}}{2 c_1} \\ y &= \frac {1+\sqrt {-4 c_1^{2} x^{2}+4 c_1 x +1}}{2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.177 (sec). Leaf size: 48

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]^2+2 K[1]-1}{(K[1]+1) \left (K[1]^2+1\right )}dK[1]=-\log (x)+c_1,y(x)\right ] \]

✓ Sympy. Time used: 2.091 (sec). Leaf size: 58

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

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