29.6.20 problem 166

Internal problem ID [4766]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 6
Problem number : 166
Date solved : Monday, January 27, 2025 at 09:36:58 AM
CAS classification : [_separable]

\begin{align*} x y^{\prime }&=a +b y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 12.568 (sec). Leaf size: 69

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

\begin{align*} y(x)\to \frac {\sqrt {a} \tan \left (\sqrt {a} \sqrt {b} (\log (x)+c_1)\right )}{\sqrt {b}} \\ y(x)\to -\frac {i \sqrt {a}}{\sqrt {b}} \\ y(x)\to \frac {i \sqrt {a}}{\sqrt {b}} \\ \end{align*}