Internal problem ID [5494]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.9. Reduction of Order. Page
38
Problem number: 3(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-1-\left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.052 (sec). Leaf size: 17
dsolve(diff(y(x),x$2)=1+(diff(y(x),x))^2,y(x), singsol=all)
\[ y \relax (x ) = -\ln \left (\sin \relax (x ) c_{1}-\cos \relax (x ) c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 2.007 (sec). Leaf size: 16
DSolve[y''[x]==1+(y'[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-\log (\cos (x+c_1)) \\ \end{align*}