Internal problem ID [6371]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 79.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 43
dsolve(diff(y(x),x) = y(x)*(1+ a^2*x/sqrt(a^2*(x^2+1)))/sqrt(a^2*(x^2+1)),y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (\frac {a^{2} x}{\sqrt {a^{2}}}+\sqrt {a^{2} x^{2}+a^{2}}\right )^{\frac {1}{\sqrt {a^{2}}}} \sqrt {x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.226 (sec). Leaf size: 61
DSolve[y'[x]== y[x]*(1+ a^2*x/Sqrt[a^2*(x^2+1)])/Sqrt[a^2*(x^2+1)],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (-\sqrt {a^2 \left (x^2+1\right )}\right ) \left (\sqrt {a^2 \left (x^2+1\right )}-\sqrt {a^2} x\right )^{-\frac {1}{\sqrt {a^2}}} \\ y(x)\to 0 \\ \end{align*}