29.11.16 problem 307

Internal problem ID [4907]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 307
Date solved : Monday, January 27, 2025 at 09:47:32 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} \left (a^{2}+x^{2}\right ) y^{\prime }+\left (x -y\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 28

dsolve((a^2+x^2)*diff(y(x),x)+(x-y(x))*y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.282 (sec). Leaf size: 37

DSolve[(x^2+a^2)D[y[x],x]+(x-y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {a^2}{-x+a^2 c_1 \sqrt {a^2+x^2}} \\ y(x)\to 0 \\ \end{align*}