Internal problem ID [3488]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 755.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-1-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.092 (sec). Leaf size: 31
dsolve(diff(y(x),x)^2 = 1+y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = -i \\ y \relax (x ) = i \\ y \relax (x ) = -\sinh \left (c_{1}-x \right ) \\ y \relax (x ) = \sinh \left (c_{1}-x \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 33.621 (sec). Leaf size: 109
DSolve[(y'[x])^2==1+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\tanh (x-c_1)}{\sqrt {\text {sech}^2(x-c_1)}} \\ y(x)\to \frac {\tanh (x-c_1)}{\sqrt {\text {sech}^2(x-c_1)}} \\ y(x)\to -\frac {\tanh (x+c_1)}{\sqrt {\text {sech}^2(x+c_1)}} \\ y(x)\to \frac {\tanh (x+c_1)}{\sqrt {\text {sech}^2(x+c_1)}} \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}