Internal problem ID [3915]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 7
Problem number: 19.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}-x -\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}=0} \]
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 145
dsolve(y(x)-1/sqrt(1+(diff(y(x),x))^2)=(x+diff(y(x),x)/sqrt(1+(diff(y(x),x))^2)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{\sqrt {{\left (\sqrt {-\frac {1}{c_{1}^{2}-2 c_{1} x +x^{2}-1}}\, c_{1} -x \sqrt {-\frac {1}{c_{1}^{2}-2 c_{1} x +x^{2}-1}}\right )}^{2}+1}}+x +\frac {\sqrt {-\frac {1}{c_{1}^{2}-2 c_{1} x +x^{2}-1}}\, c_{1} -x \sqrt {-\frac {1}{c_{1}^{2}-2 c_{1} x +x^{2}-1}}}{\sqrt {{\left (\sqrt {-\frac {1}{c_{1}^{2}-2 c_{1} x +x^{2}-1}}\, c_{1} -x \sqrt {-\frac {1}{c_{1}^{2}-2 c_{1} x +x^{2}-1}}\right )}^{2}+1}} \]
✓ Solution by Mathematica
Time used: 43.084 (sec). Leaf size: 15753
DSolve[y[x]-1/Sqrt[1+(y'[x])^2]==(x+y'[x]/Sqrt[1+(y'[x])^2]),y[x],x,IncludeSingularSolutions -> True]
Too large to display