60.1.157 problem 160

Internal problem ID [10171]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 160
Date solved : Wednesday, March 05, 2025 at 08:34:58 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} \left (x^{2}-4\right ) y^{\prime }+\left (x +2\right ) y^{2}-4 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=(x^2-4)*diff(y(x),x)+(x+2)*y(x)^2-4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x -2}{\left (\ln \left (x +2\right )+c_{1} \right ) \left (x +2\right )} \]

✓ Mathematica. Time used: 0.281 (sec). Leaf size: 134

ode=(x^2-4)*D[y[x],x] + (x+2)*y[x]^2 - 4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {\exp \left (\int _1^x\frac {4}{K[1]^2-4}dK[1]\right )}{-\int _1^x-\frac {\exp \left (\int _1^{K[2]}\frac {4}{K[1]^2-4}dK[1]\right )}{K[2]-2}dK[2]+c_1} \\ y(x)\to 0 \\ y(x)\to -\frac {\exp \left (\int _1^x\frac {4}{K[1]^2-4}dK[1]\right )}{\int _1^x-\frac {\exp \left (\int _1^{K[2]}\frac {4}{K[1]^2-4}dK[1]\right )}{K[2]-2}dK[2]} \\ \end{align*}

✓ Sympy. Time used: 0.322 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 2)*y(x)**2 + (x**2 - 4)*Derivative(y(x), x) - 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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