29.13.2 problem 356

Internal problem ID [4956]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 356
Date solved : Monday, January 27, 2025 at 09:55:48 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 25

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

\[ y \left (x \right ) = \frac {-a \,\operatorname {arctanh}\left (\frac {1}{\sqrt {x^{2}+1}}\right )+c_{1}}{\sqrt {x^{2}+1}} \]

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 31

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

\[ y(x)\to \frac {-a \text {arctanh}\left (\sqrt {x^2+1}\right )+c_1}{\sqrt {x^2+1}} \]