29.10.24 problem 290

Internal problem ID [4890]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 290
Date solved : Monday, January 27, 2025 at 09:46:37 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 17

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

\[ y(x)\to \left (x^2+1\right ) \left (x^2+c_1\right ) \]