29.9.19 problem 259

Internal problem ID [4859]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 259
Date solved : Monday, January 27, 2025 at 09:42:59 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.200 (sec). Leaf size: 75

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

\begin{align*} y(x)\to -\frac {\sqrt {a} \tan \left (\frac {\sqrt {a} \sqrt {b} (1-c_1 x)}{x}\right )}{\sqrt {b}} \\ y(x)\to -\frac {i \sqrt {a}}{\sqrt {b}} \\ y(x)\to \frac {i \sqrt {a}}{\sqrt {b}} \\ \end{align*}