29.10.23 problem 289

Internal problem ID [4889]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 289
Date solved : Monday, January 27, 2025 at 09:46:36 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 25

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

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