Internal problem ID [2298]
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: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime }+2 {y^{\prime }}^{2}=2} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)+2*diff(y(x),x)^2=2,y(x), singsol=all)
\[ y \left (x \right ) = x +\frac {\ln \left (\frac {{\mathrm e}^{-4 x} c_{1}}{2}-\frac {c_{2}}{2}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.389 (sec). Leaf size: 62
DSolve[y''[x]+2*y'[x]^2==2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-\log \left (e^{2 x}\right )+\log \left (e^{4 x}+e^{2 c_1}\right )+2 c_2\right ) y(x)\to \frac {1}{2} \left (-\log \left (e^{2 x}\right )+\log \left (e^{4 x}\right )+2 c_2\right ) \end{align*}