Internal problem ID [2299]
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: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-{y^{\prime }}^{3}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
dsolve(diff(y(x),x$2)+diff(y(x),x)=diff(y(x),x)^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\operatorname {arctanh}\left (\sqrt {-{\mathrm e}^{2 x} c_{1} +1}\right )+c_{2} y \left (x \right ) = \operatorname {arctanh}\left (\sqrt {-{\mathrm e}^{2 x} c_{1} +1}\right )+c_{2} \end{align*}
✓ Solution by Mathematica
Time used: 60.1 (sec). Leaf size: 47
DSolve[y''[x]+y'[x]==y'[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-\text {arctanh}\left (\sqrt {1+e^{2 (x+c_1)}}\right ) y(x)\to \text {arctanh}\left (\sqrt {1+e^{2 (x+c_1)}}\right )+c_2 \end{align*}