Internal problem ID [6846]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing.
EXERCISES Page 324
Problem number: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime }-{y^{\prime }}^{2}=1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)=1+diff(y(x),x)^2,y(x), singsol=all)
\[ y \left (x \right ) = -\ln \left (\frac {-c_{2} +\tan \left (x \right ) c_{1}}{\sec \left (x \right )}\right ) \]
✓ Solution by Mathematica
Time used: 1.97 (sec). Leaf size: 16
DSolve[y''[x]==1+(y'[x])^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2-\log (\cos (x+c_1)) \]