60.1.159 problem 160

Internal problem ID [10173]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 160
Date solved : Monday, January 27, 2025 at 06:31:15 PM
CAS classification : [_rational, _Bernoulli]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[(x^2-4)*D[y[x],x] + (x+2)*y[x]^2 - 4*y[x]==0,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*}