29.11.18 problem 309

Internal problem ID [4909]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 309
Date solved : Monday, January 27, 2025 at 09:50:17 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 3.988 (sec). Leaf size: 47

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

\begin{align*} y(x)\to -\frac {e^{c_1}}{-\sqrt {a^2+x^2}+b e^{c_1}} \\ y(x)\to 0 \\ y(x)\to -\frac {1}{b} \\ \end{align*}