Internal problem ID [6370]
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]
\[ \boxed {y^{\prime }-\frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}}=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = c_{1} \left (\frac {a^{2} x}{\sqrt {a^{2}}}+\sqrt {a^{2} x^{2}+a^{2}}\right )^{\frac {1}{\sqrt {a^{2}}}} \sqrt {x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.339 (sec). Leaf size: 105
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 -\frac {\sqrt {a^2} c_1 \sqrt {a^2 \left (x^2+1\right )} \left (a \left (-\sqrt {a^2 \left (x^2+1\right )}+\sqrt {a^2}+a x\right )\right )^{-1/a} \left (a \left (\sqrt {a^2 \left (x^2+1\right )}-\sqrt {a^2}+a x\right )\right )^{\frac {1}{a}}}{2 a^4} \\ y(x)\to 0 \\ \end{align*}