Internal problem ID [4416]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 7
Problem number: 11.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}=-1+\frac {\left (a +x \right )^{2}}{2 a x +x^{2}}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 42
dsolve(1+(diff(y(x),x))^2=(x+a)^2/(x^2+2*a*x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= a \ln \left (x +a +\sqrt {x \left (2 a +x \right )}\right )+c_{1} \\ y \left (x \right ) &= -a \ln \left (x +a +\sqrt {x \left (2 a +x \right )}\right )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 107
DSolve[1+(y'[x])^2==(x+a)^2/(x^2+2*a*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2 a \sqrt {x} \sqrt {2 a+x} \log \left (\sqrt {2 a+x}-\sqrt {x}\right )}{\sqrt {x (2 a+x)}}+c_1 \\ y(x)\to \frac {2 a \sqrt {x} \sqrt {2 a+x} \log \left (\sqrt {2 a+x}-\sqrt {x}\right )}{\sqrt {x (2 a+x)}}+c_1 \\ \end{align*}