60.1.148 problem 149

Internal problem ID [10162]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 149
Date solved : Monday, January 27, 2025 at 06:30:31 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

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

\[ y = \frac {x^{2}}{3}+\frac {1}{3}+\frac {c_{1}}{\sqrt {x^{2}+1}} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 27

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

\[ y(x)\to \frac {1}{3} \left (x^2+1\right )+\frac {c_1}{\sqrt {x^2+1}} \]