Internal problem ID [3908]
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]
Solve \begin {gather*} \boxed {1+\left (y^{\prime }\right )^{2}-\frac {\left (a +x \right )^{2}}{2 a x +x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.116 (sec). Leaf size: 44
dsolve(1+(diff(y(x),x))^2=(x+a)^2/(x^2+2*a*x),y(x), singsol=all)
\begin{align*} y \relax (x ) = a \ln \left (a +x +\sqrt {2 a x +x^{2}}\right )+c_{1} \\ y \relax (x ) = -a \ln \left (a +x +\sqrt {2 a x +x^{2}}\right )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 103
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} \tanh ^{-1}\left (\frac {\sqrt {x}}{\sqrt {2 a+x}}\right )}{\sqrt {x (2 a+x)}}+c_1 \\ y(x)\to \frac {2 a \sqrt {x} \sqrt {2 a+x} \tanh ^{-1}\left (\frac {\sqrt {x}}{\sqrt {2 a+x}}\right )}{\sqrt {x (2 a+x)}}+c_1 \\ \end{align*}