31.6.19 problem 19

Internal problem ID [5768]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 7
Problem number : 19
Date solved : Monday, January 27, 2025 at 01:16:08 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}&=x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \end{align*}

✓ Solution by Maple

Time used: 0.336 (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)
 

\[ y \left (x \right ) = \frac {c_{1} \sqrt {-\frac {1}{\left (x +1-c_{1} \right ) \left (x -1-c_{1} \right )}}+1}{\sqrt {-\frac {1}{\left (x +1-c_{1} \right ) \left (x -1-c_{1} \right )}}} \]

✓ Solution by Mathematica

Time used: 48.500 (sec). Leaf size: 20847

DSolve[y[x]-1/Sqrt[1+(D[y[x],x])^2]==(x+D[y[x],x]/Sqrt[1+(D[y[x],x])^2]),y[x],x,IncludeSingularSolutions -> True]
 

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