29.26.19 problem 755

Internal problem ID [5340]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 755
Date solved : Monday, January 27, 2025 at 11:15:53 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.122 (sec). Leaf size: 37

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

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