29.10.20 problem 286

Internal problem ID [4886]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 286
Date solved : Monday, January 27, 2025 at 09:46:26 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 27

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

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