Internal problem ID [7729]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 149.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }+y x -x \left (x^{2}+1\right )=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = \frac {x^{2}}{3}+\frac {1}{3}+\frac {c_{1}}{\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 27
DSolve[(x^2+1)*y'[x] + x*y[x] - x*(x^2+1)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} \left (x^2+1\right )+\frac {c_1}{\sqrt {x^2+1}} \\ \end{align*}