83.45.5 problem Ex 5 page 53

Internal problem ID [19548]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter IV. Equations of the first order but not of the first degree
Problem number : Ex 5 page 53
Date solved : Tuesday, January 28, 2025 at 01:50:39 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.178 (sec). Leaf size: 51

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

\begin{align*} y \left (x \right ) &= 1+b \\ y \left (x \right ) &= b -\sqrt {-\left (x -c_{1} +1\right ) \left (x -c_{1} -1\right )} \\ y \left (x \right ) &= b +\sqrt {-\left (x -c_{1} +1\right ) \left (x -c_{1} -1\right )} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.431 (sec). Leaf size: 124

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

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