Internal problem ID [11344]
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 9.
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: 0.016 (sec). Leaf size: 15
dsolve(diff(y(x),x$2)+diff(y(x),x)^2+1=0,y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (-c_{1} \sin \left (x \right )+c_{2} \cos \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 3.113 (sec). Leaf size: 16
DSolve[y''[x]+y'[x]^2+1==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \log (\cos (x-c_1))+c_2 \]