83.32.5 problem 5

Internal problem ID [19404]
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 (F) at page 113
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 01:38:02 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.351 (sec). Leaf size: 32

dsolve(a*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 ) &= c_{2} +a \cosh \left (\frac {x +c_{1}}{a}\right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.278 (sec). Leaf size: 19

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

\[ y(x)\to a \cosh \left (\frac {x}{a}+c_1\right )+c_2 \]