Internal problem ID [3007]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 259.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-a -b y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 28
dsolve(x^2*diff(y(x),x) = a+b*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (\frac {\sqrt {a b}\, \left (c_{1} x -1\right )}{x}\right ) \sqrt {a b}}{b} \]
✓ Solution by Mathematica
Time used: 0.175 (sec). Leaf size: 75
DSolve[x^2 y'[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*}