Internal problem ID [15202]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 14. Differential equations admitting of
depression of their order. Exercises page 107
Problem number: 344.
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: 0.0 (sec). Leaf size: 17
dsolve(diff(y(x),x$2)=1+diff(y(x),x)^2,y(x), singsol=all)
\[ y = -\ln \left (-c_{2} \cos \left (x \right )+c_{1} \sin \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 1.595 (sec). Leaf size: 16
DSolve[y''[x]==1+y'[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2-\log (\cos (x+c_1)) \]