83.22.2 problem 2

Internal problem ID [19256]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (E) at page 63
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 01:15:48 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 40

dsolve(x+diff(y(x),x)/sqrt(1+diff(y(x),x)^2)=a,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 55

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

\begin{align*} y(x)\to c_1-i \sqrt {a^2-2 a x+x^2-1} \\ y(x)\to i \sqrt {a^2-2 a x+x^2-1}+c_1 \\ \end{align*}