29.12.20 problem 339

Internal problem ID [4939]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 339
Date solved : Monday, January 27, 2025 at 09:53:04 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 42

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

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

✓ Solution by Mathematica

Time used: 25.363 (sec). Leaf size: 91

DSolve[(a+b 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 (\sqrt {A} \sqrt {B} \left (\frac {\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*}