83.18.6 problem 6

Internal problem ID [19216]
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 (A) at page 53
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 01:13:55 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 19

dsolve(diff(y(x),x)^2-2*diff(y(x),x)*cosh(x)+1=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -{\mathrm e}^{-x}+c_{1} \\ y \left (x \right ) &= {\mathrm e}^{x}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.157 (sec). Leaf size: 109

DSolve[D[y[x],x]^2-D[y[x],x]*Cosh[x]+1==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} \left (\sinh (x)-\frac {i \sqrt {3} \sqrt {7-\cosh (2 x)} E\left (i x\left |-\frac {1}{3}\right .\right )}{\sqrt {\cosh (2 x)-7}}\right )+c_1 \\ y(x)\to \frac {1}{2} \left (\sinh (x)+\frac {i \sqrt {3} \sqrt {7-\cosh (2 x)} E\left (i x\left |-\frac {1}{3}\right .\right )}{\sqrt {\cosh (2 x)-7}}\right )+c_1 \\ \end{align*}