60.1.157 problem 158

Internal problem ID [10171]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 158
Date solved : Monday, January 27, 2025 at 06:31:10 PM
CAS classification : [_separable]

\begin{align*} \left (x^{2}-1\right ) y^{\prime }+a x y^{2}+y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve((x^2-1)*diff(y(x),x) + a*x*y(x)^2 + x*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {1}{\sqrt {x -1}\, \sqrt {x +1}\, c_{1} -a} \]

✓ Solution by Mathematica

Time used: 0.336 (sec). Leaf size: 57

DSolve[(x^2-1)*D[y[x],x] + a*x*y[x]^2 + x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1] (a K[1]+1)}dK[1]\&\right ]\left [-\frac {1}{2} \log \left (1-x^2\right )+c_1\right ] \\ y(x)\to 0 \\ y(x)\to -\frac {1}{a} \\ \end{align*}