83.30.2 problem 2

Internal problem ID [19381]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (D) at page 109
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 01:36:21 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.330 (sec). Leaf size: 26

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

\begin{align*} y \left (x \right ) &= -i x +c_{1} \\ y \left (x \right ) &= i x +c_{1} \\ y \left (x \right ) &= \cosh \left (x +c_{1} \right )+c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.226 (sec). Leaf size: 13

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

\[ y(x)\to \cosh (x+c_1)+c_2 \]