Internal problem ID [2292]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 35, page 157
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime }+2 {y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(y(x),x$2)+2*diff(y(x),x)^2=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\ln \left (2 c_{1} x +2 c_{2} \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.183 (sec). Leaf size: 21
DSolve[y''[x]+2*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \log (2 x-c_1)+c_2 \]