Internal problem ID [4424]
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]
\[ \boxed {y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}-\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}=x} \]
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 49
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)
\[ y \left (x \right ) = \frac {c_{1} \sqrt {-\frac {1}{\left (-c_{1} +x +1\right ) \left (x -c_{1} -1\right )}}+1}{\sqrt {-\frac {1}{\left (-c_{1} +x +1\right ) \left (x -c_{1} -1\right )}}} \]
✓ Solution by Mathematica
Time used: 42.598 (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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