Internal problem ID [4413]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 7
Problem number: 8.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {-\sqrt {1+{y^{\prime }}^{2}}-a y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 113
dsolve(x=a*diff(y(x),x)+sqrt(1+(diff(y(x),x))^2),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {a \,x^{2}+x \sqrt {a^{2}+x^{2}-1}+\left (\ln \left (x +\sqrt {a^{2}+x^{2}-1}\right )+2 c_{1} \right ) \left (1+a \right ) \left (a -1\right )}{2 a^{2}-2} \\ y \left (x \right ) &= \frac {a \,x^{2}-x \sqrt {a^{2}+x^{2}-1}-\left (1+a \right ) \left (a -1\right ) \left (\ln \left (x +\sqrt {a^{2}+x^{2}-1}\right )-2 c_{1} \right )}{2 a^{2}-2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 113
DSolve[x==a*y'[x]+Sqrt[1+(y'[x])^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (\frac {x \left (a x-\sqrt {a^2+x^2-1}\right )}{a^2-1}+\log \left (\sqrt {a^2+x^2-1}-x\right )\right )+c_1 \\ y(x)\to \frac {1}{2} \left (\frac {x \left (\sqrt {a^2+x^2-1}+a x\right )}{a^2-1}-\log \left (\sqrt {a^2+x^2-1}-x\right )\right )+c_1 \\ \end{align*}