Internal problem ID [2823]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 68.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-x^{n} \left (a +b y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve(diff(y(x),x) = x^n*(a+b*y(x)^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (\frac {\sqrt {a b}\, \left (c_{1} n +x^{n +1}+c_{1}\right )}{n +1}\right ) \sqrt {a b}}{b} \]
✓ Solution by Mathematica
Time used: 0.303 (sec). Leaf size: 78
DSolve[y'[x]==x^n(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 {x^{n+1}}{n+1}+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*}