Internal problem ID [10318]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 62.
Summary. Page 144
Problem number: Ex 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime }-{y^{\prime }}^{2}-1=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)=diff(y(x),x)^2+1,y(x), singsol=all)
\[ y \left (x \right ) = -\ln \left (\frac {c_{1} \tan \left (x \right )-c_{2}}{\sec \left (x \right )}\right ) \]
✓ Solution by Mathematica
Time used: 1.833 (sec). Leaf size: 16
DSolve[y''[x]==y'[x]^2+1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-\log (\cos (x+c_1)) \\ \end{align*}