29.28.9 problem 807

Internal problem ID [5390]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 28
Problem number : 807
Date solved : Monday, January 27, 2025 at 11:17:52 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.046 (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: 0.046 (sec). Leaf size: 25

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

\begin{align*} y(x)\to \sinh (x)-\cosh (x)+c_1 \\ y(x)\to \sinh (x)+\cosh (x)+c_1 \\ \end{align*}