10.20 problem 286

Internal problem ID [3034]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 10
Problem number: 286.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

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

Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

dsolve((x^2+1)*diff(y(x),x) = x*(x^2+1)-x*y(x),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: 0.056 (sec). Leaf size: 27

DSolve[(1+x^2)y'[x]==x(1+x^2)-x y[x],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*}