1.152 problem 153

Internal problem ID [7733]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 153.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

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

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)
 

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

Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 21

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

\begin{align*} y(x)\to a x+c_1 \sqrt {x^2-1} \\ \end{align*}