Internal problem ID [3916]
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]
Solve \begin {gather*} \boxed {y-\frac {1}{\sqrt {\left (y^{\prime }\right )^{2}+1}}-x -\frac {y^{\prime }}{\sqrt {\left (y^{\prime }\right )^{2}+1}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.375 (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)
\[ y \relax (x ) = \frac {1}{\sqrt {\left (\sqrt {-\frac {1}{x^{2}-2 c_{1} x +c_{1}^{2}-1}}\, c_{1}-x \sqrt {-\frac {1}{x^{2}-2 c_{1} x +c_{1}^{2}-1}}\right )^{2}+1}}+x +\frac {\sqrt {-\frac {1}{x^{2}-2 c_{1} x +c_{1}^{2}-1}}\, c_{1}-x \sqrt {-\frac {1}{x^{2}-2 c_{1} x +c_{1}^{2}-1}}}{\sqrt {\left (\sqrt {-\frac {1}{x^{2}-2 c_{1} x +c_{1}^{2}-1}}\, c_{1}-x \sqrt {-\frac {1}{x^{2}-2 c_{1} x +c_{1}^{2}-1}}\right )^{2}+1}} \]
✓ Solution by Mathematica
Time used: 45.348 (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]
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