83.21.4 problem 4

Internal problem ID [19248]
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 (D) at page 57
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 01:15:36 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Solution by Maple

Time used: 0.203 (sec). Leaf size: 15

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

\[ y \left (x \right ) = c_{1} x +\sqrt {c_{1}^{2}+1} \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 25

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

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