29.13.8 problem 362

Internal problem ID [4962]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 362
Date solved : Monday, January 27, 2025 at 09:56:00 AM
CAS classification : [_linear]

\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=x -\left (5 x^{2}+3\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve(x*(x^2+1)*diff(y(x),x) = x-(5*x^2+3)*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x^{4}+4 c_{1}}{4 x^{3} \left (x^{2}+1\right )} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 26

DSolve[x(1+x^2)D[y[x],x]==x-(3+5 x^2)y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^4+4 c_1}{4 \left (x^5+x^3\right )} \]