60.1.153 problem 154

Internal problem ID [10167]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 154
Date solved : Monday, January 27, 2025 at 06:30:57 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 26

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

\[ y(x)\to \frac {\int _1^x\cos (K[1])dK[1]+c_1}{x^2-1} \]