60.1.173 problem 174

Internal problem ID [10187]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 174
Date solved : Monday, January 27, 2025 at 06:34:22 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

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

\[ y = \frac {c_{1}}{\sqrt {x^{2}+1}} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 22

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

\begin{align*} y(x)\to \frac {c_1}{\sqrt {x^2+1}} \\ y(x)\to 0 \\ \end{align*}