60.1.152 problem 153

Internal problem ID [10166]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 153
Date solved : Monday, January 27, 2025 at 06:30:55 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 21

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

\[ y(x)\to a x+c_1 \sqrt {x^2-1} \]