60.1.147 problem 148

Internal problem ID [10161]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 148
Date solved : Monday, January 27, 2025 at 06:30:29 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 16

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

\[ y = \frac {\operatorname {arcsinh}\left (x \right )+c_{1}}{\sqrt {x^{2}+1}} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 20

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

\[ y(x)\to \frac {\text {arcsinh}(x)+c_1}{\sqrt {x^2+1}} \]