1.153 problem 154

Internal problem ID [7734]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 154.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

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

Solution by Maple

Time used: 0.0 (sec). Leaf size: 19

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

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

Solution by Mathematica

Time used: 0.069 (sec). Leaf size: 18

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

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