29.13.7 problem 361

Internal problem ID [4961]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 361
Date solved : Monday, January 27, 2025 at 09:55:59 AM
CAS classification : [_linear]

\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=2-4 x^{2} y \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(x*(x^2+1)*diff(y(x),x) = 2-4*x^2*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 23

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

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