Internal problem ID [5343]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 6. Existence and uniqueness of solutions to systems and nth order equations. Page
238
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime }-1-{y^{\prime }}^{2}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 7
dsolve([diff(y(x),x$2)=1+diff(y(x),x)^2,y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (\sec \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 1.809 (sec). Leaf size: 27
DSolve[{y''[x]==1+(y'[x])^2,{y[0]==0,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\log (-\cos (x))+i \pi \\ y(x)\to -\log (\cos (x)) \\ \end{align*}