Internal problem ID [3087]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 339.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (b \,x^{2}+a \right ) y^{\prime }-A -B y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve((b*x^2+a)*diff(y(x),x) = A+B*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (\frac {\sqrt {A B}\, \left (c_{1} \sqrt {a b}+\arctan \left (\frac {x b}{\sqrt {a b}}\right )\right )}{\sqrt {a b}}\right ) \sqrt {A B}}{B} \]
✓ Solution by Mathematica
Time used: 18.381 (sec). Leaf size: 91
DSolve[(a+b x^2)y'[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} \left (\frac {\text {ArcTan}\left (\frac {\sqrt {b} x}{\sqrt {a}}\right )}{\sqrt {a} \sqrt {b}}+c_1\right )\right )}{\sqrt {B}} \\ y(x)\to -\frac {i \sqrt {A}}{\sqrt {B}} \\ y(x)\to \frac {i \sqrt {A}}{\sqrt {B}} \\ \end{align*}